rlq
Kaushik Narasimhan
7/6/2020
RLQ analysis
Prepare data
When preparing palm traits for analysis, I had to remove several variables that contained NAs for our palm species. Also, I removed the descriptive traits about the fruit, and the variable “FruitShape” because it has blank values.
Run RLQ analysis and plot data
To successfully run this, I had to remove Habitat type from our environmental variables. The problem might be the naming convention. Sarah, can you make three letter codes for these?
That’s unreadable, plotting as seperate.
Summary of RLQ analysis. How to interpret this?
## RLQ analysis
##
## Class: rlq dudi
## Call: rlq(dudiR = acpR.aravo, dudiL = afcL.aravo, dudiQ = acpQ.aravo,
## scannf = FALSE)
##
## Total inertia: 0.657
##
## Eigenvalues:
## Ax1 Ax2 Ax3 Ax4 Ax5
## 0.300155 0.228303 0.083533 0.041707 0.001744
##
## Projected inertia (%):
## Ax1 Ax2 Ax3 Ax4 Ax5
## 45.6877 34.7508 12.7148 6.3484 0.2654
##
## Cumulative projected inertia (%):
## Ax1 Ax1:2 Ax1:3 Ax1:4 Ax1:5
## 45.69 80.44 93.15 99.50 99.77
##
## (Only 5 dimensions (out of 9) are shown)
##
##
## Eigenvalues decomposition:
## eig covar sdR sdQ corr
## 1 0.3001551 0.5478641 1.034229 1.481707 0.3575146
## 2 0.2283026 0.4778102 1.084627 2.004471 0.2197734
##
## Inertia & coinertia R (acpR.aravo):
## inertia max ratio
## 1 1.069629 1.755539 0.6092881
## 12 2.246045 3.085130 0.7280229
##
## Inertia & coinertia Q (acpQ.aravo):
## inertia max ratio
## 1 2.195457 5.095305 0.4308784
## 12 6.213361 7.950625 0.7814933
##
## Correlation L (afcL.aravo):
## corr max ratio
## 1 0.3575146 0.9327084 0.3833080
## 2 0.2197734 0.8335977 0.2636445Fourth-corner analysis
From tutorial: “Fourth-corner analysis can be used to test the associations between individual traits and environmental variables. To obtain a test with a correct type I error, results of model 2 (permutation of sites, i.e. rows) and 4 (permutation of species, i.e. columns) should be combined.”
nrepet <- 999
four.comb.aravo <- fourthcorner(p_env[,-10], p_species,
p_traits, modeltype = 6, p.adjust.method.G = "none",
p.adjust.method.D = "none", nrepet = nrepet)Plotting the data: “Blue cells correspond to negative significant relationships while red cells correspond to positive significant relationships (this can be modified using the argument col).”
I used the D2 option when plotting, but others exist: stat=“D2”: the association is measured between the quantitative variable and each category separately. A correlation coefficient is used to indicate the strength of the association between the given category and the small or large values of the quantitative variable. stat=“G”: the association between the quantitative variable and the whole categorical variable is measured by a global statistic (F). stat=“D”: the association is estimated between the quantitative variable and each category separately by a measure of the within-group homogeneity. The strength of the association is indicated by the dispersion of the values of the quantitative variable for a given category.
To replot the data for multiple comparisons: “Now, we adjust p-values for multiple comparisons (here we used the fdr method using the p.adjust.4thcorner function).”
Combine both approaches
“First, a multivariate test can be applied to evaluate the global significance of the traits-environment relationships. This test is based on the total inertia of the RLQ analysis”
## class: krandtest lightkrandtest
## Monte-Carlo tests
## Call: randtest.rlq(xtest = rlq.aravo, nrepet = nrepet, modeltype = 6)
##
## Number of tests: 2
##
## Adjustment method for multiple comparisons: none
## Permutation number: 999
## Test Obs Std.Obs Alter Pvalue
## 1 Model 2 0.6569709 -0.1346780 greater 0.507
## 2 Model 4 0.6569709 -0.9536772 greater 0.829
The total inertia of RLQ analysis is equal to the SRLQ multivariate statistic defined in Dray and Legendre (2008). This statistic is returned by the fourthcorner2 function:
Srlq <- fourthcorner2(p_env[,-10], p_species, p_traits,
modeltype = 6, p.adjust.method.G = "fdr", nrepet = nrepet)
Srlq$trRLQ## Monte-Carlo test
## Call: fourthcorner2(tabR = p_env[, -10], tabL = p_species, tabQ = p_traits,
## modeltype = 6, nrepet = nrepet, p.adjust.method.G = "fdr")
##
## Observation: -8990.343
##
## Based on 999 replicates
## Simulated p-value: 0.822
## Alternative hypothesis: greater
##
## Std.Obs Expectation Variance
## -9.206018e-01 -8.990088e+03 7.649906e-02“Both approaches can be combined if RLQ scores are used to represent traits and environmental variables on a biplot. Then, significant associations revealed by the fourthcorner approach can be represented using segments (blue lines for negative associations, red lines for positive associations, see the argument col). Only traits and environmental variables that have at least one significant association are represented. Here, we apply this method using adjusted pvalues for multiple comparisons and a significant level α = 0.05.”
“Another approach is provided by the fourthcorner.rlq function and consists in testing directly the links between RLQ axes and traits (typetest=”Q.axes“) or environmental variables (typetest=”R.axes“).”
RLQ axes and traits
## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.aravo, nrepet = nrepet, modeltype = 6, typetest = "Q.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter
## 1 AxcR1 / Climb.0 Homog. 0.96134310 2.20116058 less
## 2 AxcR2 / Climb.0 Homog. 0.89121986 -0.53679743 less
## 3 AxcR1 / Climb.1 Homog. 0.03686797 -0.24848563 less
## 4 AxcR2 / Climb.1 Homog. 0.10785496 1.78642185 less
## 5 AxcR1 / Acaul.0 Homog. 1.00000000 <NA> less
## 6 AxcR2 / Acaul.0 Homog. 1.00000000 <NA> less
## 7 AxcR1 / Erect.0 Homog. 0.03686797 -0.24848563 less
## 8 AxcR2 / Erect.0 Homog. 0.10785496 1.78642185 less
## 9 AxcR1 / Erect.1 Homog. 0.96134310 2.20116058 less
## 10 AxcR2 / Erect.1 Homog. 0.89121986 -0.53679743 less
## 11 AxcR1 / StemS.0 Homog. 0.03698011 -0.82249690 less
## 12 AxcR2 / StemS.0 Homog. 0.10811460 1.69818917 less
## 13 AxcR1 / StemS.1 Homog. 0.48052421 -0.47715061 less
## 14 AxcR2 / StemS.1 Homog. 0.59926258 0.29260277 less
## 15 AxcR1 / StemS.2 Homog. 0.41908006 3.49481660 less
## 16 AxcR2 / StemS.2 Homog. 0.27599200 0.82078570 less
## 17 AxcR1 / StemA.0 Homog. 0.76595294 1.53669110 less
## 18 AxcR2 / StemA.0 Homog. 0.63295693 -1.43746503 less
## 19 AxcR1 / StemA.1 Homog. 0.20361638 0.26186245 less
## 20 AxcR2 / StemA.1 Homog. 0.32299828 0.83189141 less
## 21 AxcR1 / Leave.0 Homog. 0.72348658 2.13924819 less
## 22 AxcR2 / Leave.0 Homog. 0.52504761 -1.56755644 less
## 23 AxcR1 / Leave.1 Homog. 0.24149577 0.02111477 less
## 24 AxcR2 / Leave.1 Homog. 0.44244854 1.66729070 less
## 25 AxcR1 / MaxStemHeight_m r 0.09149172 0.68994881 two-sided
## 26 AxcR2 / MaxStemHeight_m r -0.14448147 -1.18998713 two-sided
## 27 AxcR1 / MaxStemDia_cm r 0.08749172 0.67358979 two-sided
## 28 AxcR2 / MaxStemDia_cm r -0.12934431 -1.06921687 two-sided
## 29 AxcR1 / Under.canopy Homog. 0.97761339 1.77069366 less
## 30 AxcR2 / Under.canopy Homog. 0.96901013 0.58548969 less
## 31 AxcR1 / Under.understorey Homog. 0.02065195 -0.45299627 less
## 32 AxcR2 / Under.understorey Homog. 0.03098774 -0.29627554 less
## 33 AxcR1 / AverageFruitLength_cm r 0.24503760 1.89727497 two-sided
## 34 AxcR2 / AverageFruitLength_cm r -0.12292261 -0.96520838 two-sided
## 35 AxcR1 / Fruit.large Homog. 0.42030052 2.10914139 less
## 36 AxcR2 / Fruit.large Homog. 0.51860246 2.78553943 less
## 37 AxcR1 / Fruit.small Homog. 0.55423824 2.73768704 less
## 38 AxcR2 / Fruit.small Homog. 0.46746559 1.25826119 less
## 39 AxcR1 / Consp.conspicuous Homog. 0.28302363 -1.35476992 less
## 40 AxcR2 / Consp.conspicuous Homog. 0.49950186 1.79562903 less
## 41 AxcR1 / Consp.cryptic Homog. 0.67206694 1.88678666 less
## 42 AxcR2 / Consp.cryptic Homog. 0.46811068 -0.15736019 less
## Pvalue Pvalue.adj
## 1 0.996 1
## 2 0.261 0.8150625
## 3 0.61 0.8150625
## 4 0.946 1
## 5 1 1
## 6 1 1
## 7 0.61 0.8150625
## 8 0.946 1
## 9 0.996 1
## 10 0.261 0.8150625
## 11 0.241 0.8150625
## 12 0.942 1
## 13 0.308 0.8150625
## 14 0.584 0.8150625
## 15 0.993 1
## 16 0.833 1
## 17 0.929 1
## 18 0.099 0.693
## 19 0.594 0.8150625
## 20 0.811 1
## 21 0.967 1
## 22 0.07 0.6216
## 23 0.538 0.8150625
## 24 0.966 1
## 25 0.527 0.8150625
## 26 0.264 0.8150625
## 27 0.524 0.8150625
## 28 0.296 0.8150625
## 29 0.973 1
## 30 0.713 1
## 31 0.504 0.8150625
## 32 0.571 0.8150625
## 33 0.046 0.6216
## 34 0.366 0.8150625
## 35 0.973 1
## 36 0.993 1
## 37 0.988 1
## 38 0.911 1
## 39 0.074 0.6216
## 40 0.976 1
## 41 0.944 1
## 42 0.429 0.8150625
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1RLQ axes and environmental variables
## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.aravo, nrepet = nrepet, modeltype = 6, typetest = "R.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter Pvalue
## 1 Canopy.Cover / AxcQ1 r -0.012420893 -0.08504096 two-sided 0.891
## 2 Understory.Density / AxcQ1 r -0.029892325 -0.28535590 two-sided 0.784
## 3 Leaf.Litter / AxcQ1 r 0.083803687 0.83347452 two-sided 0.432
## 4 Soil.Moisture / AxcQ1 r 0.122365689 1.10765079 two-sided 0.265
## 5 Cec / AxcQ1 r 0.046971395 1.03900906 two-sided 0.333
## 6 T50 / AxcQ1 r 0.009956983 0.17613818 two-sided 0.897
## 7 T10 / AxcQ1 r 0.304644385 1.82411195 two-sided 0.079
## 8 Canopy.Height / AxcQ1 r -0.124070105 -1.03016040 two-sided 0.331
## 9 Elevation / AxcQ1 r 0.056259879 0.43232450 two-sided 0.687
## 10 Canopy.Cover / AxcQ2 r 0.014571724 0.12684783 two-sided 0.846
## 11 Understory.Density / AxcQ2 r -0.114617370 -1.15933364 two-sided 0.27
## 12 Leaf.Litter / AxcQ2 r 0.049781194 0.49259572 two-sided 0.636
## 13 Soil.Moisture / AxcQ2 r -0.068450849 -0.84961406 two-sided 0.419
## 14 Cec / AxcQ2 r 0.027732905 0.71951008 two-sided 0.499
## 15 T50 / AxcQ2 r 0.098808237 1.14865071 two-sided 0.219
## 16 T10 / AxcQ2 r -0.062682617 -0.36973774 two-sided 0.699
## 17 Canopy.Height / AxcQ2 r -0.090071839 -0.81666971 two-sided 0.48
## 18 Elevation / AxcQ2 r 0.117191890 0.95719518 two-sided 0.367
## Pvalue.adj
## 1 0.891
## 2 0.882
## 3 0.816545454545455
## 4 0.777857142857143
## 5 0.816545454545455
## 6 0.897
## 7 0.708
## 8 0.816545454545455
## 9 0.834352941176471
## 10 0.891
## 11 0.777857142857143
## 12 0.834352941176471
## 13 0.816545454545455
## 14 0.816545454545455
## 15 0.777857142857143
## 16 0.834352941176471
## 17 0.816545454545455
## 18 0.816545454545455
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Results can be represented using a table with colors indicating significance :
Significance with axes can also be reported on the factorial map of RLQ analysis. Here, significant associations with the first axis are represented in blue, with the second axis in orange, with both axes in green (variables with no significant association are in black)
RUN 2 RLQ/4th corner: Splitting all lifestage and points with some forest cover
Run RLQ/ FQ analysis for all lifestage types
That’s unreadable, plotting as separate.
## [1] "RLQ for juveniles"
## [1] "RLQ for adults"
Summary of RLQ analysis. How to interpret this?
## RLQ analysis
##
## Class: rlq dudi
## Call: rlq(dudiR = Rjuv, dudiL = Ljuv, dudiQ = Qjuv, scannf = FALSE)
##
## Total inertia: 1.429
##
## Eigenvalues:
## Ax1 Ax2 Ax3 Ax4 Ax5
## 0.746537 0.500895 0.121014 0.054025 0.003262
##
## Projected inertia (%):
## Ax1 Ax2 Ax3 Ax4 Ax5
## 52.2481 35.0563 8.4695 3.7811 0.2283
##
## Cumulative projected inertia (%):
## Ax1 Ax1:2 Ax1:3 Ax1:4 Ax1:5
## 52.25 87.30 95.77 99.55 99.78
##
## (Only 5 dimensions (out of 9) are shown)
##
##
## Eigenvalues decomposition:
## eig covar sdR sdQ corr
## 1 0.7465371 0.8640238 1.170836 1.785317 0.4133466
## 2 0.5008948 0.7077392 1.244773 1.691688 0.3360957
##
## Inertia & coinertia R (Rjuv):
## inertia max ratio
## 1 1.370856 1.858611 0.7375703
## 12 2.920316 3.464436 0.8429412
##
## Inertia & coinertia Q (Qjuv):
## inertia max ratio
## 1 3.187357 5.160919 0.6175949
## 12 6.049164 7.993775 0.7567344
##
## Correlation L (Ljuv):
## corr max ratio
## 1 0.4133466 0.9448971 0.4374514
## 2 0.3360957 0.9087471 0.3698452## RLQ analysis
##
## Class: rlq dudi
## Call: rlq(dudiR = Radu, dudiL = Ladu, dudiQ = Qadu, scannf = FALSE)
##
## Total inertia: 1.04
##
## Eigenvalues:
## Ax1 Ax2 Ax3 Ax4 Ax5
## 0.564979 0.338546 0.115397 0.015354 0.003838
##
## Projected inertia (%):
## Ax1 Ax2 Ax3 Ax4 Ax5
## 54.314 32.546 11.094 1.476 0.369
##
## Cumulative projected inertia (%):
## Ax1 Ax1:2 Ax1:3 Ax1:4 Ax1:5
## 54.31 86.86 97.95 99.43 99.80
##
## (Only 5 dimensions (out of 10) are shown)
##
##
## Eigenvalues decomposition:
## eig covar sdR sdQ corr
## 1 0.5649794 0.7516511 1.317944 1.702729 0.3349451
## 2 0.3385457 0.5818468 1.128801 2.171484 0.2373747
##
## Inertia & coinertia R (Radu):
## inertia max ratio
## 1 1.736977 2.095715 0.8288231
## 12 3.011170 3.680365 0.8181714
##
## Inertia & coinertia Q (Qadu):
## inertia max ratio
## 1 2.899287 4.937157 0.5872382
## 12 7.614631 7.890549 0.9650318
##
## Correlation L (Ladu):
## corr max ratio
## 1 0.3349451 1.0000000 0.3349451
## 2 0.2373747 0.9128287 0.2600430Fourth-corner analysis
## [1] "FQ for juveniles"
## [1] "FQ for adults"
With adjusted p-values
## [1] "FQ for Juveniles"## [1] "FQ for Adults"
Combine both approaches
## class: krandtest lightkrandtest
## Monte-Carlo tests
## Call: randtest.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6)
##
## Number of tests: 2
##
## Adjustment method for multiple comparisons: none
## Permutation number: 999
## Test Obs Std.Obs Alter Pvalue
## 1 Model 2 1.42883 0.1299938 greater 0.373
## 2 Model 4 1.42883 -0.2833431 greater 0.569
## class: krandtest lightkrandtest
## Monte-Carlo tests
## Call: randtest.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6)
##
## Number of tests: 2
##
## Adjustment method for multiple comparisons: none
## Permutation number: 999
## Test Obs Std.Obs Alter Pvalue
## 1 Model 2 1.040218 14.1026397 greater 0.001
## 2 Model 4 1.040218 -0.1732769 greater 0.549
The total inertia of RLQ analysis is equal to the SRLQ multivariate statistic defined in Dray and Legendre (2008). This statistic is returned by the fourthcorner2 function:
## Monte-Carlo test
## Call: fourthcorner2(tabR = p_envFORCOVER, tabL = p_speciesJUV, tabQ = p_traits,
## modeltype = 6, nrepet = nrepet, p.adjust.method.G = "fdr")
##
## Observation: -8989.571
##
## Based on 848 replicates
## Simulated p-value: 0.5206125
## Alternative hypothesis: greater
##
## Std.Obs Expectation Variance
## 3.635986e-01 -1.067521e+04 2.149238e+07## Monte-Carlo test
## Call: fourthcorner2(tabR = p_envFORCOVER, tabL = p_speciesADU, tabQ = p_traits,
## modeltype = 6, nrepet = nrepet, p.adjust.method.G = "fdr")
##
## Observation: -8989.96
##
## Based on 999 replicates
## Simulated p-value: 0.469
## Alternative hypothesis: greater
##
## Std.Obs Expectation Variance
## 3.555372e-01 -1.065493e+04 2.193028e+07## [1] "juvenile"
## [1] "adult"
“Another approach is provided by the fourthcorner.rlq function and consists in testing directly the links between RLQ axes and traits (typetest=”Q.axes“) or environmental variables (typetest=”R.axes“).”
RLQ axes and traits
## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6, typetest = "Q.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter
## 1 AxcR1 / Climb.0 Homog. 0.935408906 0.96730878 less
## 2 AxcR2 / Climb.0 Homog. 0.896219686 -0.46788626 less
## 3 AxcR1 / Climb.1 Homog. 0.062673284 0.07444970 less
## 4 AxcR2 / Climb.1 Homog. 0.100874152 0.87771669 less
## 5 AxcR1 / Acaul.0 Homog. 1.000000000 <NA> less
## 6 AxcR2 / Acaul.0 Homog. 1.000000000 <NA> less
## 7 AxcR1 / Erect.0 Homog. 0.062673284 0.07444970 less
## 8 AxcR2 / Erect.0 Homog. 0.100874152 0.87771669 less
## 9 AxcR1 / Erect.1 Homog. 0.935408906 0.96730878 less
## 10 AxcR2 / Erect.1 Homog. 0.896219686 -0.46788626 less
## 11 AxcR1 / StemS.0 Homog. 0.062673284 -0.42172090 less
## 12 AxcR2 / StemS.0 Homog. 0.100874152 0.87771669 less
## 13 AxcR1 / StemS.1 Homog. 0.434638318 -0.66069204 less
## 14 AxcR2 / StemS.1 Homog. 0.515663169 -0.21398743 less
## 15 AxcR1 / StemS.2 Homog. 0.336057240 1.95516021 less
## 16 AxcR2 / StemS.2 Homog. 0.379436083 2.91532672 less
## 17 AxcR1 / StemA.0 Homog. 0.823478093 2.21574440 less
## 18 AxcR2 / StemA.0 Homog. 0.594579406 -1.47389245 less
## 19 AxcR1 / StemA.1 Homog. 0.174538043 0.04400098 less
## 20 AxcR2 / StemA.1 Homog. 0.280158884 0.47985122 less
## 21 AxcR1 / Leave.0 Homog. 0.758100818 2.24583807 less
## 22 AxcR2 / Leave.0 Homog. 0.493674666 -1.56170756 less
## 23 AxcR1 / Leave.1 Homog. 0.237514667 0.04512235 less
## 24 AxcR2 / Leave.1 Homog. 0.419778917 1.50727468 less
## 25 AxcR1 / MaxStemHeight_m r -0.210341823 -1.33485794 two-sided
## 26 AxcR2 / MaxStemHeight_m r -0.077264855 -0.60188406 two-sided
## 27 AxcR1 / MaxStemDia_cm r -0.214542329 -1.34534367 two-sided
## 28 AxcR2 / MaxStemDia_cm r -0.059720466 -0.50256913 two-sided
## 29 AxcR1 / Under.canopy Homog. 0.980841113 0.92303525 less
## 30 AxcR2 / Under.canopy Homog. 0.982255001 1.08882504 less
## 31 AxcR1 / Under.understorey Homog. 0.017971110 -0.50703885 less
## 32 AxcR2 / Under.understorey Homog. 0.017628019 -0.52176153 less
## 33 AxcR1 / AverageFruitLength_cm r -0.411890001 -2.72154411 two-sided
## 34 AxcR2 / AverageFruitLength_cm r -0.004254722 -0.05040763 two-sided
## 35 AxcR1 / Fruit.large Homog. 0.384995644 1.64637176 less
## 36 AxcR2 / Fruit.large Homog. 0.464108800 2.20963518 less
## 37 AxcR1 / Fruit.small Homog. 0.515842044 2.27569208 less
## 38 AxcR2 / Fruit.small Homog. 0.534845101 2.63988352 less
## 39 AxcR1 / Consp.conspicuous Homog. 0.273692963 -1.14915964 less
## 40 AxcR2 / Consp.conspicuous Homog. 0.460961375 1.47668390 less
## 41 AxcR1 / Consp.cryptic Homog. 0.718840507 2.13546153 less
## 42 AxcR2 / Consp.cryptic Homog. 0.448132549 -0.23765943 less
## Pvalue Pvalue.adj
## 1 0.834 1
## 2 0.239 0.939555555555556
## 3 0.729545454545454 0.953181818181818
## 4 0.816 1
## 5 1 1
## 6 1 1
## 7 0.729545454545454 0.953181818181818
## 8 0.816 1
## 9 0.834 1
## 10 0.239 0.939555555555556
## 11 0.48991935483871 0.939555555555556
## 12 0.816 1
## 13 0.29 0.939555555555556
## 14 0.435 0.939555555555556
## 15 0.94 1
## 16 0.982 1
## 17 0.984 1
## 18 0.088 0.7476
## 19 0.573 0.939555555555556
## 20 0.672 1
## 21 0.976 1
## 22 0.089 0.7476
## 23 0.54 0.939555555555556
## 24 0.951 1
## 25 0.2 0.939555555555556
## 26 0.577 1
## 27 0.198 0.939555555555556
## 28 0.664 1
## 29 0.817 1
## 30 0.867 1
## 31 0.500576701268743 0.939555555555556
## 32 0.567474048442907 0.939555555555556
## 33 0.001 0.042 *
## 34 0.967 1
## 35 0.944 1
## 36 0.976 1
## 37 0.967 1
## 38 0.985 1
## 39 0.136 0.939555555555556
## 40 0.953 1
## 41 0.97 1
## 42 0.424 0.939555555555556
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6, typetest = "Q.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter
## 1 AxcR1 / Climb.0 Homog. 0.836672753 -1.25688155 less
## 2 AxcR2 / Climb.0 Homog. 0.940072279 0.35896830 less
## 3 AxcR1 / Climb.1 Homog. 0.074800140 0.75299442 less
## 4 AxcR2 / Climb.1 Homog. 0.056918191 -0.05118715 less
## 5 AxcR1 / Acaul.0 Homog. 1.000000000 <NA> less
## 6 AxcR2 / Acaul.0 Homog. 1.000000000 <NA> less
## 7 AxcR1 / Erect.0 Homog. 0.074800140 0.75299442 less
## 8 AxcR2 / Erect.0 Homog. 0.056918191 -0.05118715 less
## 9 AxcR1 / Erect.1 Homog. 0.836672753 -1.25688155 less
## 10 AxcR2 / Erect.1 Homog. 0.940072279 0.35896830 less
## 11 AxcR1 / StemS.0 Homog. 0.100179857 2.12995286 less
## 12 AxcR2 / StemS.0 Homog. 0.061059378 -0.48373717 less
## 13 AxcR1 / StemS.1 Homog. 0.641005501 0.57497054 less
## 14 AxcR2 / StemS.1 Homog. 0.722324576 1.17791479 less
## 15 AxcR1 / StemS.2 Homog. 0.155320246 -0.92942985 less
## 16 AxcR2 / StemS.2 Homog. 0.193553765 -0.63288592 less
## 17 AxcR1 / StemA.0 Homog. 0.656649208 1.80265637 less
## 18 AxcR2 / StemA.0 Homog. 0.629379796 0.73860010 less
## 19 AxcR1 / StemA.1 Homog. 0.312689117 1.17801079 less
## 20 AxcR2 / StemA.1 Homog. 0.363941396 1.34293539 less
## 21 AxcR1 / Leave.0 Homog. 0.510919122 -1.69942334 less
## 22 AxcR2 / Leave.0 Homog. 0.566988117 0.85126100 less
## 23 AxcR1 / Leave.1 Homog. 0.488493502 1.01718767 less
## 24 AxcR2 / Leave.1 Homog. 0.421492370 1.17374967 less
## 25 AxcR1 / MaxStemHeight_m r 0.088990901 0.55193677 two-sided
## 26 AxcR2 / MaxStemHeight_m r 0.252057476 2.13834988 two-sided
## 27 AxcR1 / MaxStemDia_cm r -0.035464815 -0.25817726 two-sided
## 28 AxcR2 / MaxStemDia_cm r 0.258239812 2.20446456 two-sided
## 29 AxcR1 / Under.canopy Homog. 0.940406773 0.47747322 less
## 30 AxcR2 / Under.canopy Homog. 0.949032509 1.00781417 less
## 31 AxcR1 / Under.understorey Homog. 0.058403035 0.07372075 less
## 32 AxcR2 / Under.understorey Homog. 0.049026243 -0.16777458 less
## 33 AxcR1 / AverageFruitLength_cm r -0.004633307 -0.16778394 two-sided
## 34 AxcR2 / AverageFruitLength_cm r 0.158137536 1.37845374 two-sided
## 35 AxcR1 / Fruit.large Homog. 0.463222263 2.50854387 less
## 36 AxcR2 / Fruit.large Homog. 0.558166806 0.48794982 less
## 37 AxcR1 / Fruit.small Homog. 0.534548704 2.61819964 less
## 38 AxcR2 / Fruit.small Homog. 0.400441438 -1.69145817 less
## 39 AxcR1 / Consp.conspicuous Homog. 0.559426785 1.05934370 less
## 40 AxcR2 / Consp.conspicuous Homog. 0.506219974 0.04933554 less
## 41 AxcR1 / Consp.cryptic Homog. 0.439722847 -0.26063794 less
## 42 AxcR2 / Consp.cryptic Homog. 0.473926570 -0.05589842 less
## Pvalue Pvalue.adj
## 1 0.127 0.654
## 2 0.598 0.966
## 3 0.791 1
## 4 0.793397231096912 1
## 5 1 1
## 6 1 1
## 7 0.791 1
## 8 0.793397231096912 1
## 9 0.127 0.654
## 10 0.598 0.966
## 11 0.974 1
## 12 0.495 1
## 13 0.681 1
## 14 0.881 1
## 15 0.218 0.654
## 16 0.345 0.905625
## 17 0.966 1
## 18 0.77 1
## 19 0.854 1
## 20 0.881 1
## 21 0.056 0.4704
## 22 0.802 1
## 23 0.842 1
## 24 0.887 1
## 25 0.631 1
## 26 0.004 0.084 .
## 27 0.791 1
## 28 0.002 0.084 .
## 29 0.664 1
## 30 0.84 1
## 31 0.647497337593184 1
## 32 0.647497337593184 1
## 33 0.868 1
## 34 0.197 0.654
## 35 0.981 1
## 36 0.688 1
## 37 0.996 1
## 38 0.043 0.168
## 39 0.855 1
## 40 0.538 1
## 41 0.41 0.956666666666667
## 42 0.483 1
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1RLQ axes and environmental variables
## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6, typetest = "R.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter Pvalue Pvalue.adj
## 1 Canopy.Cover / AxcQ1 r -0.023925899 -0.1934982 two-sided 0.793 0.906285714285714
## 2 Understory.Density / AxcQ1 r -0.046616337 -0.3474136 two-sided 0.763 0.906285714285714
## 3 Leaf.Litter / AxcQ1 r -0.004365802 -0.0126180 two-sided 0.987 0.987
## 4 Soil.Moisture / AxcQ1 r -0.220288874 -1.6287285 two-sided 0.11 0.377142857142857
## 5 Cec / AxcQ1 r -0.021245562 -0.1654269 two-sided 0.739 0.906285714285714
## 6 T50 / AxcQ1 r 0.050329640 0.6670247 two-sided 0.555 0.830181818181818
## 7 T10 / AxcQ1 r -0.314893261 -1.4962719 two-sided 0.135 0.648
## 8 Canopy.Height / AxcQ1 r 0.080491140 0.5959590 two-sided 0.586 0.830181818181818
## 9 Elevation / AxcQ1 r 0.074152550 0.5241494 two-sided 0.629 0.838666666666667
## 10 Habit.Primary / AxcQ1 Homog. 0.339462103 -1.5132647 less 0.087 0.522
## 11 Habit.Secondary / AxcQ1 Homog. 0.586665219 1.2752312 less 0.886 0.924521739130435
## 12 Habit.Transition / AxcQ1 Homog. 0.005065871 -0.3037668 less 0.434 0.801230769230769
## 13 Canopy.Cover / AxcQ2 r -0.077862187 -1.1990435 two-sided 0.25 0.690666666666667
## 14 Understory.Density / AxcQ2 r -0.189627260 -1.6219673 two-sided 0.11 0.377142857142857
## 15 Leaf.Litter / AxcQ2 r 0.155590484 1.1873636 two-sided 0.259 0.690666666666667
## 16 Soil.Moisture / AxcQ2 r -0.067983135 -0.5704121 two-sided 0.618 0.830181818181818
## 17 Cec / AxcQ2 r 0.052327639 0.8462091 two-sided 0.423 0.801230769230769
## 18 T50 / AxcQ2 r 0.153959525 1.5089620 two-sided 0.176 0.474666666666667
## 19 T10 / AxcQ2 r 0.119721332 0.5934057 two-sided 0.587 0.830181818181818
## 20 Canopy.Height / AxcQ2 r -0.132627095 -1.0155636 two-sided 0.36 0.785454545454545
## 21 Elevation / AxcQ2 r 0.213975341 1.4183420 two-sided 0.176 0.690666666666667
## 22 Habit.Primary / AxcQ2 Homog. 0.548269612 1.2032756 less 0.882 0.922434782608696
## 23 Habit.Secondary / AxcQ2 Homog. 0.448034986 -0.5104000 less 0.298 0.7152
## 24 Habit.Transition / AxcQ2 Homog. 0.003669394 -0.7159396 less 0.203 0.690666666666667
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6, typetest = "R.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter Pvalue Pvalue.adj
## 1 Canopy.Cover / AxcQ1 r -0.020525343 -0.52987608 two-sided 0.593 0.884210526315789
## 2 Understory.Density / AxcQ1 r 0.176408140 1.90263412 two-sided 0.066 0.6384
## 3 Leaf.Litter / AxcQ1 r -0.050385708 -0.56929404 two-sided 0.642 0.884210526315789
## 4 Soil.Moisture / AxcQ1 r -0.201383111 -1.92812765 two-sided 0.084 0.6384
## 5 Cec / AxcQ1 r -0.032244658 -0.69057769 two-sided 0.552 0.884210526315789
## 6 T50 / AxcQ1 r 0.062841701 1.54634036 two-sided 0.133 0.6384
## 7 T10 / AxcQ1 r 0.104356069 1.04877602 two-sided 0.335 0.884210526315789
## 8 Canopy.Height / AxcQ1 r -0.079818074 -0.61186294 two-sided 0.53 0.884210526315789
## 9 Elevation / AxcQ1 r 0.292632454 1.94190843 two-sided 0.061 0.6384
## 10 Habit.Primary / AxcQ1 Homog. 0.616404905 3.82920806 less 1 1
## 11 Habit.Secondary / AxcQ1 Homog. 0.351213487 0.06348844 less 0.453 0.884210526315789
## 12 Habit.Transition / AxcQ1 Homog. 0.020031880 1.01380927 less 0.89 0.970909090909091
## 13 Canopy.Cover / AxcQ2 r -0.059842511 -1.41144181 two-sided 0.177 0.685714285714286
## 14 Understory.Density / AxcQ2 r -0.043046543 -0.55372181 two-sided 0.589 0.884210526315789
## 15 Leaf.Litter / AxcQ2 r 0.116980880 1.34077455 two-sided 0.2 0.685714285714286
## 16 Soil.Moisture / AxcQ2 r -0.059469654 -0.50494174 two-sided 0.671 0.884210526315789
## 17 Cec / AxcQ2 r 0.003349974 0.07791062 two-sided 0.949 1
## 18 T50 / AxcQ2 r -0.015681784 -0.42301126 two-sided 0.7 0.884210526315789
## 19 T10 / AxcQ2 r 0.114251067 0.99929615 two-sided 0.404 0.884210526315789
## 20 Canopy.Height / AxcQ2 r 0.185686323 1.51680403 two-sided 0.122 0.6384
## 21 Elevation / AxcQ2 r 0.006309089 0.11471122 two-sided 0.901 1
## 22 Habit.Primary / AxcQ2 Homog. 0.671935150 7.51254013 less 1 1
## 23 Habit.Secondary / AxcQ2 Homog. 0.315497275 -0.70813760 less 0.244 0.732
## 24 Habit.Transition / AxcQ2 Homog. 0.011255924 0.97553325 less 0.842 0.962285714285714
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Results can be represented using a table with colors indicating significance :
## [1] "juveniles"
## [1] "adults"
Significance with axes can also be reported on the factorial map of RLQ analysis. Here, significant associations with the first axis are represented in blue, with the second axis in orange, with both axes in green (variables with no significant association are in black)
## [1] "juveniles"
## [1] "adults"
RUN 3 RLQ/4th corner : Sarah data with endemism, distance to edge
First,Checking to see which environmental variables may be removed. Next, adding “endemism” as a trait and distance to edge as an environmental variable. Also, removing acualescence as a trait because it is 0 for all species
Run RLQ/ FQ analysis for all lifestage types with aforementioned additions and subtractions
That’s unreadable, plotting as separate.
## [1] "RLQ for juveniles"
## [1] "RLQ for adults"
Summary of RLQ analysis. How to interpret this?
## RLQ analysis
##
## Class: rlq dudi
## Call: rlq(dudiR = Rjuv, dudiL = Ljuv, dudiQ = Qjuv, scannf = FALSE)
##
## Total inertia: 1.841
##
## Eigenvalues:
## Ax1 Ax2 Ax3 Ax4 Ax5
## 1.023276 0.568427 0.177298 0.058006 0.008741
##
## Projected inertia (%):
## Ax1 Ax2 Ax3 Ax4 Ax5
## 55.5733 30.8708 9.6289 3.1503 0.4747
##
## Cumulative projected inertia (%):
## Ax1 Ax1:2 Ax1:3 Ax1:4 Ax1:5
## 55.57 86.44 96.07 99.22 99.70
##
## (Only 5 dimensions (out of 10) are shown)
##
##
## Eigenvalues decomposition:
## eig covar sdR sdQ corr
## 1 1.0232755 1.0115708 1.156079 1.984850 0.4408401
## 2 0.5684266 0.7539407 1.319574 1.742581 0.3278766
##
## Inertia & coinertia R (Rjuv):
## inertia max ratio
## 1 1.336519 2.083847 0.6413710
## 12 3.077794 3.706795 0.8303113
##
## Inertia & coinertia Q (Qjuv):
## inertia max ratio
## 1 3.939629 5.923820 0.6650487
## 12 6.976219 8.831465 0.7899277
##
## Correlation L (Ljuv):
## corr max ratio
## 1 0.4408401 0.9448971 0.4665483
## 2 0.3278766 0.9087471 0.3608007## RLQ analysis
##
## Class: rlq dudi
## Call: rlq(dudiR = Radu, dudiL = Ladu, dudiQ = Qadu, scannf = FALSE)
##
## Total inertia: 1.206
##
## Eigenvalues:
## Ax1 Ax2 Ax3 Ax4 Ax5
## 0.625507 0.413324 0.138729 0.015854 0.008632
##
## Projected inertia (%):
## Ax1 Ax2 Ax3 Ax4 Ax5
## 51.880 34.281 11.506 1.315 0.716
##
## Cumulative projected inertia (%):
## Ax1 Ax1:2 Ax1:3 Ax1:4 Ax1:5
## 51.88 86.16 97.67 98.98 99.70
##
## (Only 5 dimensions (out of 11) are shown)
##
##
## Eigenvalues decomposition:
## eig covar sdR sdQ corr
## 1 0.6255075 0.7908903 1.343610 1.753889 0.3356146
## 2 0.4133241 0.6429029 1.160387 2.273361 0.2437105
##
## Inertia & coinertia R (Radu):
## inertia max ratio
## 1 1.805288 2.102328 0.8587091
## 12 3.151785 3.976897 0.7925237
##
## Inertia & coinertia Q (Qadu):
## inertia max ratio
## 1 3.076127 5.622196 0.5471398
## 12 8.244298 8.644041 0.9537551
##
## Correlation L (Ladu):
## corr max ratio
## 1 0.3356146 1.0000000 0.3356146
## 2 0.2437105 0.9128287 0.2669838Fourth-corner analysis
## [1] "FQ for juveniles"
## [1] "FQ for adults"
With adjusted p-values
## [1] "FQ for Juveniles"## [1] "FQ for Adults"
Combine both approaches
## class: krandtest lightkrandtest
## Monte-Carlo tests
## Call: randtest.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6)
##
## Number of tests: 2
##
## Adjustment method for multiple comparisons: none
## Permutation number: 999
## Test Obs Std.Obs Alter Pvalue
## 1 Model 2 1.841307 0.3269977 greater 0.308
## 2 Model 4 1.841307 -0.2176873 greater 0.537
## class: krandtest lightkrandtest
## Monte-Carlo tests
## Call: randtest.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6)
##
## Number of tests: 2
##
## Adjustment method for multiple comparisons: none
## Permutation number: 999
## Test Obs Std.Obs Alter Pvalue
## 1 Model 2 1.205686 14.64756906 greater 0.001
## 2 Model 4 1.205686 -0.01226891 greater 0.445
The total inertia of RLQ analysis is equal to the SRLQ multivariate statistic defined in Dray and Legendre (2008). This statistic is returned by the fourthcorner2 function:
## Monte-Carlo test
## Call: fourthcorner2(tabR = p_envFORCOVER1, tabL = p_speciesJUV, tabQ = p_traits1,
## modeltype = 6, nrepet = nrepet, p.adjust.method.G = "fdr")
##
## Observation: 1.841307
##
## Based on 866 replicates
## Simulated p-value: 0.4821223
## Alternative hypothesis: greater
##
## Std.Obs Expectation Variance
## 3.796293e-01 -2.120580e+03 3.125675e+07## Monte-Carlo test
## Call: fourthcorner2(tabR = p_envFORCOVER1, tabL = p_speciesADU, tabQ = p_traits1,
## modeltype = 6, nrepet = nrepet, p.adjust.method.G = "fdr")
##
## Observation: 1.205686
##
## Based on 999 replicates
## Simulated p-value: 0.437
## Alternative hypothesis: greater
##
## Std.Obs Expectation Variance
## 3.518998e-01 -1.858790e+03 2.793739e+07## [1] "juvenile"
## [1] "adult"
“Another approach is provided by the fourthcorner.rlq function and consists in testing directly the links between RLQ axes and traits (typetest=”Q.axes“) or environmental variables (typetest=”R.axes“).”
RLQ axes and traits
## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6, typetest = "Q.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter
## 1 AxcR1 / Climb.0 Homog. 0.942945338 1.48955097 less
## 2 AxcR2 / Climb.0 Homog. 0.887966514 -0.59997125 less
## 3 AxcR1 / Climb.1 Homog. 0.056778645 0.02739841 less
## 4 AxcR2 / Climb.1 Homog. 0.105016974 1.16022486 less
## 5 AxcR1 / Erect.0 Homog. 0.056778645 0.02739841 less
## 6 AxcR2 / Erect.0 Homog. 0.105016974 1.16022486 less
## 7 AxcR1 / Erect.1 Homog. 0.942945338 1.48955097 less
## 8 AxcR2 / Erect.1 Homog. 0.887966514 -0.59997125 less
## 9 AxcR1 / StemS.0 Homog. 0.056778645 -0.47648041 less
## 10 AxcR2 / StemS.0 Homog. 0.105016974 1.16022486 less
## 11 AxcR1 / StemS.1 Homog. 0.378007330 -1.07900945 less
## 12 AxcR2 / StemS.1 Homog. 0.516340283 -0.19846384 less
## 13 AxcR1 / StemS.2 Homog. 0.387906143 3.21675214 less
## 14 AxcR2 / StemS.2 Homog. 0.370412761 2.74352823 less
## 15 AxcR1 / StemA.0 Homog. 0.846477367 3.09498570 less
## 16 AxcR2 / StemA.0 Homog. 0.575515278 -1.76021815 less
## 17 AxcR1 / StemA.1 Homog. 0.144787247 -0.15351120 less
## 18 AxcR2 / StemA.1 Homog. 0.299882800 0.98097504 less
## 19 AxcR1 / Leave.0 Homog. 0.789697817 3.19983827 less
## 20 AxcR2 / Leave.0 Homog. 0.469877648 -1.87227466 less
## 21 AxcR1 / Leave.1 Homog. 0.204478037 -0.14070792 less
## 22 AxcR2 / Leave.1 Homog. 0.453892607 2.24680886 less
## 23 AxcR1 / MaxStemHeight_m r -0.237983875 -1.38869769 two-sided
## 24 AxcR2 / MaxStemHeight_m r -0.062809900 -0.54446733 two-sided
## 25 AxcR1 / MaxStemDia_cm r -0.258486176 -1.49884247 two-sided
## 26 AxcR2 / MaxStemDia_cm r -0.037868601 -0.37259370 two-sided
## 27 AxcR1 / Under.canopy Homog. 0.979333980 0.63907480 less
## 28 AxcR2 / Under.canopy Homog. 0.982526948 1.23934198 less
## 29 AxcR1 / Under.understorey Homog. 0.019166192 -0.50686561 less
## 30 AxcR2 / Under.understorey Homog. 0.017367006 -0.53605206 less
## 31 AxcR1 / AverageFruitLength_cm r -0.452199286 -2.66812273 two-sided
## 32 AxcR2 / AverageFruitLength_cm r 0.003499081 -0.02457669 two-sided
## 33 AxcR1 / Fruit.large Homog. 0.331292318 1.38097008 less
## 34 AxcR2 / Fruit.large Homog. 0.464895306 2.21126148 less
## 35 AxcR1 / Fruit.small Homog. 0.541998666 3.01590566 less
## 36 AxcR2 / Fruit.small Homog. 0.534797422 2.67965943 less
## 37 AxcR1 / Consp.conspicuous Homog. 0.233700288 -1.51675543 less
## 38 AxcR2 / Consp.conspicuous Homog. 0.494657715 2.16285249 less
## 39 AxcR1 / Consp.cryptic Homog. 0.756266600 3.14054575 less
## 40 AxcR2 / Consp.cryptic Homog. 0.425049000 -0.42163574 less
## 41 AxcR1 / Endem.N Homog. 0.639298606 2.06545772 less
## 42 AxcR2 / Endem.N Homog. 0.680103140 2.66844709 less
## 43 AxcR1 / Endem.Y Homog. 0.253670980 0.64930376 less
## 44 AxcR2 / Endem.Y Homog. 0.302646743 0.89467698 less
## Pvalue Pvalue.adj
## 1 0.946 1
## 2 0.302 0.897111111111111
## 3 0.719862227324914 0.897111111111111
## 4 0.881 1
## 5 0.719862227324914 0.897111111111111
## 6 0.881 1
## 7 0.946 1
## 8 0.302 0.897111111111111
## 9 0.449144008056395 0.897111111111111
## 10 0.881 1
## 11 0.152 0.743111111111111
## 12 0.445 0.897111111111111
## 13 0.997 1
## 14 0.979 1
## 15 1 1
## 16 0.08 0.586666666666667
## 17 0.496 0.897111111111111
## 18 0.856 1
## 19 1 1
## 20 0.035 0.385
## 21 0.469 0.897111111111111
## 22 0.992 1
## 23 0.188 0.752
## 24 0.63 1
## 25 0.134 0.737
## 26 0.741 1
## 27 0.73 1
## 28 0.905 1
## 29 0.350620067643743 0.897111111111111
## 30 0.489289740698985 0.897111111111111
## 31 0.001 0.044 *
## 32 0.987 1
## 33 0.903 0.969073170731707
## 34 0.983 0.994
## 35 0.997 1
## 36 0.979 1
## 37 0.062 0.5456
## 38 0.994 1
## 39 1 1
## 40 0.339 0.897111111111111
## 41 0.97 1
## 42 0.988 1
## 43 0.724 0.897111111111111
## 44 0.799 0.92625641025641
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6, typetest = "Q.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter
## 1 AxcR1 / Climb.0 Homog. 0.83878800 -1.30723241 less
## 2 AxcR2 / Climb.0 Homog. 0.92806148 -0.15870374 less
## 3 AxcR1 / Climb.1 Homog. 0.06572084 0.25077239 less
## 4 AxcR2 / Climb.1 Homog. 0.07149187 0.15373177 less
## 5 AxcR1 / Erect.0 Homog. 0.06572084 0.25077239 less
## 6 AxcR2 / Erect.0 Homog. 0.07149187 0.15373177 less
## 7 AxcR1 / Erect.1 Homog. 0.83878800 -1.30723241 less
## 8 AxcR2 / Erect.1 Homog. 0.92806148 -0.15870374 less
## 9 AxcR1 / StemS.0 Homog. 0.08634274 1.45429776 less
## 10 AxcR2 / StemS.0 Homog. 0.07955566 -0.32243170 less
## 11 AxcR1 / StemS.1 Homog. 0.66796398 0.63412063 less
## 12 AxcR2 / StemS.1 Homog. 0.69889719 0.70656856 less
## 13 AxcR1 / StemS.2 Homog. 0.14292688 -0.95832218 less
## 14 AxcR2 / StemS.2 Homog. 0.19780660 -0.64140843 less
## 15 AxcR1 / StemA.0 Homog. 0.64819924 1.90621972 less
## 16 AxcR2 / StemA.0 Homog. 0.63371818 0.92643152 less
## 17 AxcR1 / StemA.1 Homog. 0.32949836 1.19692392 less
## 18 AxcR2 / StemA.1 Homog. 0.34779593 1.14522352 less
## 19 AxcR1 / Leave.0 Homog. 0.50199245 -1.68234120 less
## 20 AxcR2 / Leave.0 Homog. 0.56216172 0.71461362 less
## 21 AxcR1 / Leave.1 Homog. 0.49796240 1.70501202 less
## 22 AxcR2 / Leave.1 Homog. 0.42274621 1.12993989 less
## 23 AxcR1 / MaxStemHeight_m r 0.02822684 0.14462996 two-sided
## 24 AxcR2 / MaxStemHeight_m r 0.27328220 4.20085607 two-sided
## 25 AxcR1 / MaxStemDia_cm r -0.09391981 -0.74048106 two-sided
## 26 AxcR2 / MaxStemDia_cm r 0.24057327 3.72207317 two-sided
## 27 AxcR1 / Under.canopy Homog. 0.92833279 -0.06790975 less
## 28 AxcR2 / Under.canopy Homog. 0.94839654 1.02776366 less
## 29 AxcR1 / Under.understorey Homog. 0.07160547 0.22822596 less
## 30 AxcR2 / Under.understorey Homog. 0.04773318 -0.20530624 less
## 31 AxcR1 / AverageFruitLength_cm r -0.03484667 -0.30060237 two-sided
## 32 AxcR2 / AverageFruitLength_cm r 0.13177768 2.06803281 two-sided
## 33 AxcR1 / Fruit.large Homog. 0.47695492 2.27801726 less
## 34 AxcR2 / Fruit.large Homog. 0.55907817 2.55787399 less
## 35 AxcR1 / Fruit.small Homog. 0.51644087 2.56572753 less
## 36 AxcR2 / Fruit.small Homog. 0.41516517 -1.34524089 less
## 37 AxcR1 / Consp.conspicuous Homog. 0.56082793 1.36421707 less
## 38 AxcR2 / Consp.conspicuous Homog. 0.50700928 0.05660122 less
## 39 AxcR1 / Consp.cryptic Homog. 0.43912858 -0.31372726 less
## 40 AxcR2 / Consp.cryptic Homog. 0.46947184 -0.16310900 less
## 41 AxcR1 / Endem.N Homog. 0.75809032 3.98678484 less
## 42 AxcR2 / Endem.N Homog. 0.61165270 -1.35390305 less
## 43 AxcR1 / Endem.Y Homog. 0.22906109 0.39937785 less
## 44 AxcR2 / Endem.Y Homog. 0.34266653 1.06890026 less
## Pvalue Pvalue.adj
## 1 0.109 0.509666666666667
## 2 0.244 0.715733333333333
## 3 0.822033898305085 0.9504
## 4 0.742584745762712 0.9504
## 5 0.822033898305085 0.9504
## 6 0.742584745762712 0.9504
## 7 0.109 0.509666666666667
## 8 0.244 0.715733333333333
## 9 0.921 1
## 10 0.535 0.9504
## 11 0.714 0.9504
## 12 0.73 0.9504
## 13 0.201 0.680307692307692
## 14 0.339 0.858
## 15 0.969 1
## 16 0.823 0.978702702702703
## 17 0.864 0.9504
## 18 0.847 0.9504
## 19 0.065 0.476666666666667
## 20 0.753 0.933777777777778
## 21 0.962 1
## 22 0.856 0.9504
## 23 0.904 0.970146341463415
## 24 0.001 0.022 *
## 25 0.497 0.9504
## 26 0.001 0.022 *
## 27 0.39 0.858
## 28 0.863 0.999263157894737
## 29 0.801937567276642 0.9504
## 30 0.652314316469322 0.9504
## 31 0.771 0.9504
## 32 0.026 0.286
## 33 0.965 0.987441860465116
## 34 0.993 0.993
## 35 0.991 1
## 36 0.092 0.240705882352941
## 37 0.923 1
## 38 0.522 0.9504
## 39 0.373 0.858
## 40 0.451 0.944952380952381
## 41 1 1
## 42 0.104 0.509666666666667
## 43 0.629 0.9504
## 44 0.818 0.9504
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1RLQ axes and environmental variables
## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6, typetest = "R.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter Pvalue Pvalue.adj
## 1 Canopy.Cover / AxcQ1 r -0.027082001 -0.52572294 two-sided 0.624 0.8203
## 2 Understory.Density / AxcQ1 r -0.044211965 -0.30560298 two-sided 0.771 0.871565217391304
## 3 Leaf.Litter / AxcQ1 r -0.010738222 -0.06114232 two-sided 0.963 0.963
## 4 Soil.Moisture / AxcQ1 r -0.209217633 -1.51378360 two-sided 0.143 0.4108
## 5 Cec / AxcQ1 r -0.020003447 -0.15142763 two-sided 0.732 0.865090909090909
## 6 T50 / AxcQ1 r 0.052092111 0.74240510 two-sided 0.542 0.8203
## 7 T10 / AxcQ1 r -0.291256964 -1.37676923 two-sided 0.18 0.676
## 8 Canopy.Height / AxcQ1 r 0.052059100 0.34893759 two-sided 0.727 0.865090909090909
## 9 Elevation / AxcQ1 r 0.081603760 0.57128024 two-sided 0.631 0.8203
## 10 Habit.Primary / AxcQ1 Homog. 0.360502141 -1.33297633 less 0.12 0.676
## 11 Habit.Secondary / AxcQ1 Homog. 0.563310431 1.08656815 less 0.845 0.915416666666667
## 12 Habit.Transition / AxcQ1 Homog. 0.005027318 -0.28359018 less 0.437 0.811571428571429
## 13 DIST_TO_EDGE / AxcQ1 r 0.211399707 1.33190186 two-sided 0.204 0.676
## 14 Canopy.Cover / AxcQ2 r -0.072770002 -1.12448052 two-sided 0.268 0.676
## 15 Understory.Density / AxcQ2 r -0.194407978 -1.65451142 two-sided 0.104 0.4108
## 16 Leaf.Litter / AxcQ2 r 0.151367486 1.20861256 two-sided 0.241 0.676
## 17 Soil.Moisture / AxcQ2 r -0.084135297 -0.75148220 two-sided 0.491 0.8203
## 18 Cec / AxcQ2 r 0.051703131 0.86588195 two-sided 0.412 0.811571428571429
## 19 T50 / AxcQ2 r 0.154079461 1.59755261 two-sided 0.134 0.4108
## 20 T10 / AxcQ2 r 0.095251330 0.49062813 two-sided 0.593 0.8203
## 21 Canopy.Height / AxcQ2 r -0.116196765 -0.89974896 two-sided 0.419 0.811571428571429
## 22 Elevation / AxcQ2 r 0.231792556 1.56103010 two-sided 0.135 0.676
## 23 Habit.Primary / AxcQ2 Homog. 0.553105221 1.29699940 less 0.888 0.92352
## 24 Habit.Secondary / AxcQ2 Homog. 0.443104025 -0.53116941 less 0.286 0.676
## 25 Habit.Transition / AxcQ2 Homog. 0.003596493 -0.69412740 less 0.221 0.676
## 26 DIST_TO_EDGE / AxcQ2 r -0.105836495 -0.72644932 two-sided 0.52 0.8203
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6, typetest = "R.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter Pvalue Pvalue.adj
## 1 Canopy.Cover / AxcQ1 r 0.001624833 0.01188009 two-sided 0.996 1
## 2 Understory.Density / AxcQ1 r 0.183169313 2.04512755 two-sided 0.052 0.450666666666667
## 3 Leaf.Litter / AxcQ1 r -0.077384180 -0.88510802 two-sided 0.448 0.8424
## 4 Soil.Moisture / AxcQ1 r -0.172881503 -1.75543586 two-sided 0.104 0.557555555555556
## 5 Cec / AxcQ1 r -0.024907637 -0.56776530 two-sided 0.63 0.862105263157895
## 6 T50 / AxcQ1 r 0.060254130 1.46780160 two-sided 0.156 0.557555555555556
## 7 T10 / AxcQ1 r 0.047907682 0.56727786 two-sided 0.571 0.853666666666667
## 8 Canopy.Height / AxcQ1 r -0.142726818 -1.17130836 two-sided 0.193 0.557555555555556
## 9 Elevation / AxcQ1 r 0.284330712 1.96491924 two-sided 0.049 0.450666666666667
## 10 Habit.Primary / AxcQ1 Homog. 0.605796029 4.91290425 less 1 1
## 11 Habit.Secondary / AxcQ1 Homog. 0.357932430 0.09193709 less 0.486 0.8424
## 12 Habit.Transition / AxcQ1 Homog. 0.027512005 1.19323539 less 0.903 0.968
## 13 DIST_TO_EDGE / AxcQ1 r 0.131878851 2.11377531 two-sided 0.031 0.450666666666667
## 14 Canopy.Cover / AxcQ2 r -0.063037019 -1.56385893 two-sided 0.109 0.557555555555556
## 15 Understory.Density / AxcQ2 r -0.013923655 -0.24386228 two-sided 0.828 0.938260869565217
## 16 Leaf.Litter / AxcQ2 r 0.090256890 1.09225112 two-sided 0.323 0.763454545454545
## 17 Soil.Moisture / AxcQ2 r -0.089557654 -0.78517218 two-sided 0.453 0.8424
## 18 Cec / AxcQ2 r -0.013858236 -0.28140853 two-sided 0.813 0.938260869565217
## 19 T50 / AxcQ2 r 0.003854337 0.05085136 two-sided 0.944 1
## 20 T10 / AxcQ2 r 0.151584504 1.38250213 two-sided 0.188 0.557555555555556
## 21 Canopy.Height / AxcQ2 r 0.176425383 1.49153334 two-sided 0.136 0.557555555555556
## 22 Elevation / AxcQ2 r 0.041118048 0.22344554 two-sided 0.83 0.938260869565217
## 23 Habit.Primary / AxcQ2 Homog. 0.675289384 7.62222694 less 1 1
## 24 Habit.Secondary / AxcQ2 Homog. 0.316239141 -0.56272059 less 0.285 0.741
## 25 Habit.Transition / AxcQ2 Homog. 0.006115840 -0.08677965 less 0.591 0.853666666666667
## 26 DIST_TO_EDGE / AxcQ2 r -0.035825991 -0.63558022 two-sided 0.562 0.853666666666667
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Results can be represented using a table with colors indicating significance :
## [1] "juveniles"
## [1] "adults"
Significance with axes can also be reported on the factorial map of RLQ analysis. Here, significant associations with the first axis are represented in blue, with the second axis in orange, with both axes in green (variables with no significant association are in black)
## [1] "juveniles"
## [1] "adults"
RUN 4: RLQ/4th corner: Including Luke’s data, broken down by age, converted to Denisities
Run RLQ/ FQ analysis for all lifestage types COMBINED DATA
That’s unreadable, plotting as separate.
## [1] "RLQ for juveniles"
## [1] "RLQ for adults"
Summary of RLQ analysis. How to interpret this?
## RLQ analysis
##
## Class: rlq dudi
## Call: rlq(dudiR = Rjuv, dudiL = Ljuv, dudiQ = Qjuv, scannf = FALSE)
##
## Total inertia: 0.5071
##
## Eigenvalues:
## Ax1 Ax2 Ax3 Ax4 Ax5
## 0.30533 0.11443 0.06096 0.02369 0.00200
##
## Projected inertia (%):
## Ax1 Ax2 Ax3 Ax4 Ax5
## 60.2072 22.5644 12.0197 4.6722 0.3943
##
## Cumulative projected inertia (%):
## Ax1 Ax1:2 Ax1:3 Ax1:4 Ax1:5
## 60.21 82.77 94.79 99.46 99.86
##
## (Only 5 dimensions (out of 8) are shown)
##
##
## Eigenvalues decomposition:
## eig covar sdR sdQ corr
## 1 0.3053304 0.5525671 1.063631 1.508370 0.3444183
## 2 0.1144315 0.3382772 1.111907 1.627049 0.1869837
##
## Inertia & coinertia R (Rjuv):
## inertia max ratio
## 1 1.131310 1.408984 0.8029265
## 12 2.367647 2.673132 0.8857201
##
## Inertia & coinertia Q (Qjuv):
## inertia max ratio
## 1 2.275181 3.708939 0.6134317
## 12 4.922468 6.934943 0.7098066
##
## Correlation L (Ljuv):
## corr max ratio
## 1 0.3444183 0.8781144 0.3922248
## 2 0.1869837 0.8370330 0.2233887## RLQ analysis
##
## Class: rlq dudi
## Call: rlq(dudiR = Radu, dudiL = Ladu, dudiQ = Qadu, scannf = FALSE)
##
## Total inertia: 0.3568
##
## Eigenvalues:
## Ax1 Ax2 Ax3 Ax4 Ax5
## 0.192475 0.086756 0.067868 0.005586 0.002817
##
## Projected inertia (%):
## Ax1 Ax2 Ax3 Ax4 Ax5
## 53.9414 24.3135 19.0201 1.5656 0.7894
##
## Cumulative projected inertia (%):
## Ax1 Ax1:2 Ax1:3 Ax1:4 Ax1:5
## 53.94 78.25 97.27 98.84 99.63
##
## (Only 5 dimensions (out of 8) are shown)
##
##
## Eigenvalues decomposition:
## eig covar sdR sdQ corr
## 1 0.19247487 0.4387196 1.086161 1.913300 0.2111105
## 2 0.08675598 0.2945437 1.102252 1.403553 0.1903882
##
## Inertia & coinertia R (Radu):
## inertia max ratio
## 1 1.179745 1.387695 0.8501476
## 12 2.394704 2.740164 0.8739273
##
## Inertia & coinertia Q (Qadu):
## inertia max ratio
## 1 3.660716 4.077184 0.8978541
## 12 5.630678 7.312295 0.7700288
##
## Correlation L (Ladu):
## corr max ratio
## 1 0.2111105 1.0000000 0.2111105
## 2 0.1903882 0.9480088 0.2008296Fourth-corner analysis
## [1] "FQ for juveniles"
## [1] "FQ for adults"
With adjusted p-values
## [1] "FQ for Juveniles"## [1] "FQ for Adults"
Combine both approaches
## class: krandtest lightkrandtest
## Monte-Carlo tests
## Call: randtest.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6)
##
## Number of tests: 2
##
## Adjustment method for multiple comparisons: none
## Permutation number: 999
## Test Obs Std.Obs Alter Pvalue
## 1 Model 2 0.507133 11.23012548 greater 0.001
## 2 Model 4 0.507133 0.06700219 greater 0.450
## class: krandtest lightkrandtest
## Monte-Carlo tests
## Call: randtest.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6)
##
## Number of tests: 2
##
## Adjustment method for multiple comparisons: none
## Permutation number: 999
## Test Obs Std.Obs Alter Pvalue
## 1 Model 2 0.3568223 12.0699667 greater 0.001
## 2 Model 4 0.3568223 0.9624644 greater 0.174
The total inertia of RLQ analysis is equal to the SRLQ multivariate statistic defined in Dray and Legendre (2008). This statistic is returned by the fourthcorner2 function:
## Monte-Carlo test
## Call: fourthcorner2(tabR = p_envCombined, tabL = JuvCombined, tabQ = p_traits2,
## modeltype = 6, nrepet = nrepet, p.adjust.method.G = "fdr")
##
## Observation: 0.507133
##
## Based on 943 replicates
## Simulated p-value: 0.4597458
## Alternative hypothesis: greater
##
## Std.Obs Expectation Variance
## 0.04949982 0.49969574 0.02257454## Monte-Carlo test
## Call: fourthcorner2(tabR = p_envCombined, tabL = AduCombined, tabQ = p_traits2,
## modeltype = 6, nrepet = nrepet, p.adjust.method.G = "fdr")
##
## Observation: 0.3568223
##
## Based on 999 replicates
## Simulated p-value: 0.166
## Alternative hypothesis: greater
##
## Std.Obs Expectation Variance
## 5.000727e-01 -2.399700e+03 2.303439e+07## [1] "juvenile"
## [1] "adult"
“Another approach is provided by the fourthcorner.rlq function and consists in testing directly the links between RLQ axes and traits (typetest=”Q.axes“) or environmental variables (typetest=”R.axes“).”
RLQ axes and traits
## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6, typetest = "Q.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter
## 1 AxcR1 / Climb.0 Homog. 0.950691650 0.02297862 less
## 2 AxcR2 / Climb.0 Homog. 0.941841026 -0.16365303 less
## 3 AxcR1 / Climb.1 Homog. 0.033731565 -0.11523651 less
## 4 AxcR2 / Climb.1 Homog. 0.049479519 1.45852361 less
## 5 AxcR1 / Erect.0 Homog. 0.033731565 -0.11523651 less
## 6 AxcR2 / Erect.0 Homog. 0.049479519 1.45852361 less
## 7 AxcR1 / Erect.1 Homog. 0.950691650 0.02297862 less
## 8 AxcR2 / Erect.1 Homog. 0.941841026 -0.16365303 less
## 9 AxcR1 / StemS.0 Homog. 0.042486336 -0.62407515 less
## 10 AxcR2 / StemS.0 Homog. 0.059233726 1.32029688 less
## 11 AxcR1 / StemS.1 Homog. 0.600092020 0.06909407 less
## 12 AxcR2 / StemS.1 Homog. 0.663529348 0.98963052 less
## 13 AxcR1 / StemS.2 Homog. 0.337273734 1.95226449 less
## 14 AxcR2 / StemS.2 Homog. 0.267940716 -0.22206955 less
## 15 AxcR1 / StemA.0 Homog. 0.413618760 0.96874178 less
## 16 AxcR2 / StemA.0 Homog. 0.409856391 0.54901906 less
## 17 AxcR1 / StemA.1 Homog. 0.572991793 3.04965858 less
## 18 AxcR2 / StemA.1 Homog. 0.587847629 3.42208062 less
## 19 AxcR1 / Leave.0 Homog. 0.354248320 -0.12272264 less
## 20 AxcR2 / Leave.0 Homog. 0.353383576 -0.08334301 less
## 21 AxcR1 / Leave.1 Homog. 0.616579602 2.85114226 less
## 22 AxcR2 / Leave.1 Homog. 0.646520452 3.38539337 less
## 23 AxcR1 / MaxStemHeight_m r -0.081641368 -0.51410952 two-sided
## 24 AxcR2 / MaxStemHeight_m r 0.019080907 0.27036126 two-sided
## 25 AxcR1 / MaxStemDia_cm r -0.111440071 -0.69917296 two-sided
## 26 AxcR2 / MaxStemDia_cm r 0.051767377 0.65718792 two-sided
## 27 AxcR1 / Under.canopy Homog. 0.825995793 -0.21400969 less
## 28 AxcR2 / Under.canopy Homog. 0.824299326 -0.29534801 less
## 29 AxcR1 / Under.understorey Homog. 0.131796389 -0.01477115 less
## 30 AxcR2 / Under.understorey Homog. 0.173736036 0.37677877 less
## 31 AxcR1 / AverageFruitLength_cm r 0.003639056 0.03905259 two-sided
## 32 AxcR2 / AverageFruitLength_cm r 0.139110582 1.60663803 two-sided
## 33 AxcR1 / Fruit.large Homog. 0.171370100 -0.07021277 less
## 34 AxcR2 / Fruit.large Homog. 0.225979472 0.40238496 less
## 35 AxcR1 / Fruit.small Homog. 0.816271465 3.55292068 less
## 36 AxcR2 / Fruit.small Homog. 0.742787554 -0.65533486 less
## 37 AxcR1 / Consp.conspicuous Homog. 0.665815314 1.43610990 less
## 38 AxcR2 / Consp.conspicuous Homog. 0.699872302 1.90444340 less
## 39 AxcR1 / Consp.cryptic Homog. 0.317460710 0.87173520 less
## 40 AxcR2 / Consp.cryptic Homog. 0.298427569 -0.28843876 less
## 41 AxcR1 / Endem.N Homog. 0.722721789 -0.14631779 less
## 42 AxcR2 / Endem.N Homog. 0.720851064 -0.26717447 less
## 43 AxcR1 / Endem.Y Homog. 0.191637919 -0.40711010 less
## 44 AxcR2 / Endem.Y Homog. 0.272932571 0.59682909 less
## Pvalue Pvalue.adj
## 1 0.342 0.875111111111111
## 2 0.45 0.875111111111111
## 3 0.680896478121665 0.881160148157449
## 4 0.931 0.985395348837209
## 5 0.680896478121665 0.881160148157449
## 6 0.931 0.985395348837209
## 7 0.342 0.875111111111111
## 8 0.45 0.875111111111111
## 9 0.345 0.875111111111111
## 10 0.908 0.985395348837209
## 11 0.493 0.875111111111111
## 12 0.855 0.985395348837209
## 13 0.963 0.985395348837209
## 14 0.428 0.875111111111111
## 15 0.824 0.979891891891892
## 16 0.725 0.935314285714286
## 17 0.999 1
## 18 1 1
## 19 0.461 0.743285714285714
## 20 0.473 0.743285714285714
## 21 0.997 1
## 22 1 1
## 23 0.649 0.881160148157449
## 24 0.81 0.963243243243243
## 25 0.514 0.875111111111111
## 26 0.535 0.875111111111111
## 27 0.352 0.875111111111111
## 28 0.368 0.875111111111111
## 29 0.568 0.881160148157449
## 30 0.647 0.881160148157449
## 31 0.978 1
## 32 0.102 0.641142857142857
## 33 0.537 0.875111111111111
## 34 0.652 0.881160148157449
## 35 1 1
## 36 0.245 0.875111111111111
## 37 0.924 1
## 38 0.976 1
## 39 0.796 0.972888888888889
## 40 0.396 0.69696
## 41 0.422 0.875111111111111
## 42 0.394 0.875111111111111
## 43 0.389 0.875111111111111
## 44 0.744 0.935314285714286
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6, typetest = "Q.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter
## 1 AxcR1 / Climb.0 Homog. 0.97179858 0.914152396 less
## 2 AxcR2 / Climb.0 Homog. 0.97948921 2.604089304 less
## 3 AxcR1 / Climb.1 Homog. 0.02531189 -0.352455173 less
## 4 AxcR2 / Climb.1 Homog. 0.01348188 -0.589989143 less
## 5 AxcR1 / Erect.0 Homog. 0.02531189 -0.352455173 less
## 6 AxcR2 / Erect.0 Homog. 0.01348188 -0.589989143 less
## 7 AxcR1 / Erect.1 Homog. 0.97179858 0.914152396 less
## 8 AxcR2 / Erect.1 Homog. 0.97948921 2.604089304 less
## 9 AxcR1 / StemS.0 Homog. 0.04679292 -0.460331662 less
## 10 AxcR2 / StemS.0 Homog. 0.04346445 -0.591578392 less
## 11 AxcR1 / StemS.1 Homog. 0.47268434 -0.679161415 less
## 12 AxcR2 / StemS.1 Homog. 0.53370050 3.049384513 less
## 13 AxcR1 / StemS.2 Homog. 0.46353583 0.994016377 less
## 14 AxcR2 / StemS.2 Homog. 0.41647109 0.851510796 less
## 15 AxcR1 / StemA.0 Homog. 0.21466306 -1.191998737 less
## 16 AxcR2 / StemA.0 Homog. 0.29338290 3.790097450 less
## 17 AxcR1 / StemA.1 Homog. 0.78478607 1.201653576 less
## 18 AxcR2 / StemA.1 Homog. 0.69891091 3.317531288 less
## 19 AxcR1 / Leave.0 Homog. 0.18698199 -0.871186511 less
## 20 AxcR2 / Leave.0 Homog. 0.26528813 4.371985909 less
## 21 AxcR1 / Leave.1 Homog. 0.81301791 0.915403428 less
## 22 AxcR2 / Leave.1 Homog. 0.71751015 2.856201824 less
## 23 AxcR1 / MaxStemHeight_m r -0.11128831 -1.473647834 two-sided
## 24 AxcR2 / MaxStemHeight_m r -0.04326206 -0.598501338 two-sided
## 25 AxcR1 / MaxStemDia_cm r -0.16305380 -2.163140637 two-sided
## 26 AxcR2 / MaxStemDia_cm r -0.02330345 -0.293644047 two-sided
## 27 AxcR1 / Under.canopy Homog. 0.84135842 -0.061285857 less
## 28 AxcR2 / Under.canopy Homog. 0.84882465 0.912217124 less
## 29 AxcR1 / Under.understorey Homog. 0.15371029 0.063375226 less
## 30 AxcR2 / Under.understorey Homog. 0.14529232 -0.001334491 less
## 31 AxcR1 / AverageFruitLength_cm r -0.20867857 -2.765443755 two-sided
## 32 AxcR2 / AverageFruitLength_cm r 0.03378664 0.527096705 two-sided
## 33 AxcR1 / Fruit.large Homog. 0.21701516 0.134072032 less
## 34 AxcR2 / Fruit.large Homog. 0.22896442 0.253936793 less
## 35 AxcR1 / Fruit.small Homog. 0.74297350 -0.364222176 less
## 36 AxcR2 / Fruit.small Homog. 0.76496435 -0.263594037 less
## 37 AxcR1 / Consp.conspicuous Homog. 0.76188172 1.391075196 less
## 38 AxcR2 / Consp.conspicuous Homog. 0.72621006 1.411520681 less
## 39 AxcR1 / Consp.cryptic Homog. 0.23058913 -0.512603616 less
## 40 AxcR2 / Consp.cryptic Homog. 0.27337586 1.916362313 less
## 41 AxcR1 / Endem.N Homog. 0.83942871 0.420995017 less
## 42 AxcR2 / Endem.N Homog. 0.85125177 1.396776241 less
## 43 AxcR1 / Endem.Y Homog. 0.15572888 -0.514687259 less
## 44 AxcR2 / Endem.Y Homog. 0.13859593 -0.751428706 less
## Pvalue Pvalue.adj
## 1 0.819 1
## 2 0.999 1
## 3 0.50308261405672 0.870941176470588
## 4 0.316892725030826 0.870941176470588
## 5 0.50308261405672 0.870941176470588
## 6 0.316892725030826 0.870941176470588
## 7 0.819 1
## 8 0.999 1
## 9 0.425334706488157 0.870941176470588
## 10 0.377960865087539 0.870941176470588
## 11 0.305 0.870941176470588
## 12 1 1
## 13 0.78 0.91821052631579
## 14 0.793 0.91821052631579
## 15 0.112 0.289882352941176
## 16 1 1
## 17 0.893 1
## 18 1 1
## 19 0.191 0.442315789473684
## 20 1 1
## 21 0.823 1
## 22 1 1
## 23 0.155 0.757777777777778
## 24 0.569 0.870941176470588
## 25 0.02 0.146666666666667
## 26 0.77 0.91821052631579
## 27 0.324 0.870941176470588
## 28 0.82 1
## 29 0.670670670670671 0.870941176470588
## 30 0.607607607607608 0.870941176470588
## 31 0.002 0.0176 *
## 32 0.581 0.870941176470588
## 33 0.673 0.870941176470588
## 34 0.655 0.870941176470588
## 35 0.254 0.870941176470588
## 36 0.343 0.870941176470588
## 37 0.924 1
## 38 0.924 1
## 39 0.321 0.614086956521739
## 40 0.962 1
## 41 0.648 0.891
## 42 0.92 1
## 43 0.388 0.870941176470588
## 44 0.266 0.870941176470588
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1RLQ axes and environmental variables
## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6, typetest = "R.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter Pvalue Pvalue.adj
## 1 Under.dense / AxcQ1 Homog. 0.221464258 0.327772208 less 0.743 0.8916
## 2 Under.low / AxcQ1 Homog. 0.218403774 -0.813982319 less 0.191 0.42975
## 3 Under.medium / AxcQ1 Homog. 0.550063386 1.365268845 less 0.923 0.997
## 4 Cec / AxcQ1 r 0.042828674 1.293053664 two-sided 0.123 0.339428571428571
## 5 T50 / AxcQ1 r -0.000714878 0.007297674 two-sided 0.997 0.997
## 6 T10 / AxcQ1 r -0.026242242 -0.815171179 two-sided 0.397 0.7146
## 7 Canopy.Height / AxcQ1 r -0.043252066 -0.639468467 two-sided 0.54 0.694285714285714
## 8 Elevation / AxcQ1 r 0.343316027 2.188200528 two-sided 0.009 0.108
## 9 DIST_TO_EDGE / AxcQ1 r 0.043264696 0.712888388 two-sided 0.506 0.694285714285714
## 10 Under.dense / AxcQ2 Homog. 0.271414040 2.285892891 less 0.978 0.997
## 11 Under.low / AxcQ2 Homog. 0.208125884 -1.563276630 less 0.061 0.216
## 12 Under.medium / AxcQ2 Homog. 0.513648363 0.136618803 less 0.501 0.7515
## 13 Cec / AxcQ2 r -0.043906956 -1.249087138 two-sided 0.132 0.339428571428571
## 14 T50 / AxcQ2 r -0.017580374 -0.500141307 two-sided 0.554 0.767076923076923
## 15 T10 / AxcQ2 r 0.024502707 0.711369310 two-sided 0.464 0.7515
## 16 Canopy.Height / AxcQ2 r 0.153488306 2.266352612 two-sided 0.012 0.108
## 17 Elevation / AxcQ2 r 0.019284269 0.162401495 two-sided 0.894 0.986
## 18 DIST_TO_EDGE / AxcQ2 r 0.098216141 1.802778491 two-sided 0.071 0.216
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6, typetest = "R.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter Pvalue Pvalue.adj
## 1 Under.dense / AxcQ1 Homog. 0.214360348 -0.03128674 less 0.502 0.695076923076923
## 2 Under.low / AxcQ1 Homog. 0.306199419 1.62081624 less 0.974 0.974
## 3 Under.medium / AxcQ1 Homog. 0.476937675 -1.30113594 less 0.103 0.3708
## 4 Cec / AxcQ1 r 0.031433924 1.12053990 two-sided 0.264 0.396
## 5 T50 / AxcQ1 r -0.007846279 -0.27933305 two-sided 0.779 0.876375
## 6 T10 / AxcQ1 r -0.132361714 -1.99303642 two-sided 0.01 0.066 .
## 7 Canopy.Height / AxcQ1 r -0.152381058 -1.91431680 two-sided 0.011 0.066 .
## 8 Elevation / AxcQ1 r 0.084566234 1.25240235 two-sided 0.224 0.504
## 9 DIST_TO_EDGE / AxcQ1 r -0.033692825 -0.45611548 two-sided 0.73 0.846
## 10 Under.dense / AxcQ2 Homog. 0.233712304 0.57698290 less 0.745 0.876375
## 11 Under.low / AxcQ2 Homog. 0.286539392 0.38202529 less 0.66 0.848571428571429
## 12 Under.medium / AxcQ2 Homog. 0.476587859 -1.02035920 less 0.167 0.429428571428571
## 13 Cec / AxcQ2 r -0.005443898 -0.16437119 two-sided 0.854 0.899
## 14 T50 / AxcQ2 r -0.030475271 -0.94304199 two-sided 0.352 0.6336
## 15 T10 / AxcQ2 r 0.036422985 0.53148379 two-sided 0.675 0.846
## 16 Canopy.Height / AxcQ2 r 0.050444774 0.62290993 two-sided 0.613 0.846
## 17 Elevation / AxcQ2 r 0.175774038 2.57900815 two-sided 0.006 0.066 .
## 18 DIST_TO_EDGE / AxcQ2 r 0.071782890 1.05208457 two-sided 0.336 0.6336
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Results can be represented using a table with colors indicating significance :
## [1] "juveniles"
## [1] "adults"
Significance with axes can also be reported on the factorial map of RLQ analysis. Here, significant associations with the first axis are represented in blue, with the second axis in orange, with both axes in green (variables with no significant association are in black)
## [1] "juveniles"
## [1] "adults"
RUN 5: Only Luke’s data as abundances
## 'data.frame': 19 obs. of 12 variables:
## $ Climbing : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 2 1 ...
## $ Erect : Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 2 1 2 ...
## $ StemSolitary : Factor w/ 3 levels "0","1","2": 2 2 2 3 3 3 2 2 1 3 ...
## $ StemArmed : Factor w/ 2 levels "0","1": 2 2 1 2 2 2 1 1 1 1 ...
## $ LeavesArmed : Factor w/ 2 levels "0","1": 2 2 1 2 2 2 1 1 2 1 ...
## $ MaxStemHeight_m : num 4.5 15 35 10 18 10 10 4.5 20 3 ...
## $ MaxStemDia_cm : num 6 30 60 8 25 10 8 3 3 3.4 ...
## $ UnderstoreyCanopy : Factor w/ 2 levels "canopy","understorey": 2 1 1 1 1 1 1 2 1 2 ...
## $ AverageFruitLength_cm: num 0.75 5.5 5 2 5 ...
## $ FruitSizeCategorical : Factor w/ 2 levels "large","small": 2 1 1 2 1 2 2 2 2 2 ...
## $ Conspicuousness : Factor w/ 2 levels "conspicuous",..: 2 1 2 1 1 1 1 2 1 2 ...
## $ Endemic : Factor w/ 2 levels "N","Y": 2 1 2 1 1 1 1 1 1 1 ...## 'data.frame': 2300 obs. of 7 variables:
## $ ELEV : num 414 413 412 411 411 409 407 406 405 405 ...
## $ DIST_TO_EDGE: num 1.5 6 11.4 16.6 23.3 28.5 33.5 38.2 40.6 44.2 ...
## $ CANOPY : num 25 25 31 28 25 23 7 21 25 20 ...
## $ TEN : num 5 3 4 3 5 5 4 4 4 5 ...
## $ FIFTY : num 0 0 0 1 0 0 0 0 0 0 ...
## $ CECR : num 0 0 0 0 0 0 0 0 1 0 ...
## $ UNDERSTORY : Factor w/ 3 levels "dense","low",..: 1 1 1 1 1 1 1 3 3 3 ...## 'data.frame': 2300 obs. of 19 variables:
## $ AST : num 0 0 0 0 1 0 0 0 0 0 ...
## $ AT : num 0 0 0 0 0 0 0 0 0 0 ...
## $ ATT : num 0 0 0 0 0 0 0 0 0 0 ...
## $ BATCO: num 0 0 0 0 0 0 0 3 0 0 ...
## $ BATSE: num 0 0 0 0 0 0 0 0 0 0 ...
## $ BG : num 0 0 0 0 0 0 0 0 0 0 ...
## $ CHAM : num 0 0 0 0 0 0 0 0 0 0 ...
## $ CP : num 0 0 0 0 0 0 0 0 0 0 ...
## $ DESM : num 0 0 0 0 0 0 0 0 0 0 ...
## $ IR : num 0 0 1 0 1 0 0 0 2 0 ...
## $ ONE : num 0 2 0 2 2 0 0 0 0 0 ...
## $ PHD : num 0 0 0 0 0 0 0 0 0 0 ...
## $ PHOL : num 1 0 2 0 0 0 0 0 0 0 ...
## $ PRDE : num 0 0 0 0 0 0 0 0 0 0 ...
## $ SOC : num 0 0 0 0 0 0 0 1 0 1 ...
## $ SYN : num 0 0 1 0 0 0 0 1 0 0 ...
## $ TAG : num 0 0 1 3 2 0 0 0 0 0 ...
## $ WET : num 0 0 0 0 0 0 0 0 0 0 ...
## $ GO : num 0 0 1 0 1 0 0 0 1 0 ...## 'data.frame': 2300 obs. of 18 variables:
## $ AST : num 0 0 0 0 0 0 0 0 0 0 ...
## $ AT : num 0 0 0 0 0 0 0 0 0 0 ...
## $ BATCO: num 0 0 0 0 0 0 0 0 0 0 ...
## $ BATSE: num 0 0 0 0 0 0 0 0 0 0 ...
## $ BG : num 0 0 0 0 0 0 0 0 0 0 ...
## $ CHAM : num 0 0 0 0 0 0 0 0 0 0 ...
## $ CP : num 0 0 0 1 0 0 0 0 0 0 ...
## $ DESM : num 0 0 0 0 0 0 0 0 0 0 ...
## $ IR : num 0 0 0 0 0 0 0 0 0 1 ...
## $ ONE : num 0 0 0 0 0 0 0 0 0 0 ...
## $ PHD : num 0 0 0 0 0 0 0 0 0 0 ...
## $ PHOL : num 0 0 0 0 0 0 0 0 0 0 ...
## $ PRDE : num 0 0 0 0 0 0 0 0 0 0 ...
## $ SOC : num 0 0 0 0 0 0 0 0 0 0 ...
## $ SYN : num 0 0 0 0 0 0 0 0 0 0 ...
## $ TAG : num 0 0 0 0 0 0 0 0 0 0 ...
## $ WET : num 0 0 0 0 0 0 0 0 0 0 ...
## $ GO : num 0 0 0 0 0 0 0 0 0 0 ...## Climbing Erect StemSolitary StemArmed LeavesArmed MaxStemHeight_m
## AT 0 1 1 1 1 4.5
## AST 0 1 1 1 1 15.0
## BATCO 0 1 2 1 1 10.0
## BG 0 1 2 1 1 18.0
## BATSE 0 1 2 1 1 10.0
## CHAM 0 1 1 0 0 10.0
## CP 0 1 1 0 0 4.5
## DESM 1 0 0 0 1 20.0
## GO 0 1 2 0 0 3.0
## IR 0 1 1 0 0 30.0
## ONE 0 1 1 0 0 26.0
## PHD 0 1 1 0 0 10.0
## PHOL 0 1 1 0 0 12.0
## TAG 0 1 1 0 0 15.0
## PRDE 0 1 2 0 0 10.0
## SOC 0 1 1 0 0 20.0
## SYN 0 1 0 0 0 6.0
## WET 0 1 1 0 0 10.0
## MaxStemDia_cm UnderstoreyCanopy AverageFruitLength_cm
## AT 6.0 understorey 0.750
## AST 30.0 canopy 5.500
## BATCO 8.0 canopy 2.000
## BG 25.0 canopy 5.000
## BATSE 10.0 canopy 1.900
## CHAM 8.0 canopy 1.650
## CP 3.0 understorey 1.250
## DESM 3.0 canopy 1.823
## GO 3.4 understorey 0.760
## IR 70.0 canopy 2.350
## ONE 45.0 canopy 3.500
## PHD 12.0 canopy 1.215
## PHOL 22.0 canopy 1.385
## TAG 30.0 canopy 7.500
## PRDE 12.0 canopy 0.900
## SOC 20.0 canopy 3.000
## SYN 5.0 canopy 2.350
## WET 13.0 canopy 2.500
## FruitSizeCategorical Conspicuousness Endemic
## AT small cryptic Y
## AST large conspicuous N
## BATCO small conspicuous N
## BG large conspicuous N
## BATSE small conspicuous N
## CHAM small conspicuous N
## CP small cryptic N
## DESM small conspicuous N
## GO small cryptic N
## IR small conspicuous N
## ONE small cryptic N
## PHD small conspicuous Y
## PHOL small cryptic N
## TAG large cryptic Y
## PRDE small cryptic N
## SOC small cryptic N
## SYN small conspicuous N
## WET small conspicuous YRun RLQ/ FQ analysis for all lifestage types COMBINED DATA
That’s unreadable, plotting as separate.
## [1] "RLQ for juveniles"
## [1] "RLQ for adults"
Summary of RLQ analysis. How to interpret this?
## RLQ analysis
##
## Class: rlq dudi
## Call: rlq(dudiR = Rjuv, dudiL = Ljuv, dudiQ = Qjuv, scannf = FALSE)
##
## Total inertia: 0.3496
##
## Eigenvalues:
## Ax1 Ax2 Ax3 Ax4 Ax5
## 0.253201 0.051745 0.029468 0.009449 0.002748
##
## Projected inertia (%):
## Ax1 Ax2 Ax3 Ax4 Ax5
## 72.431 14.802 8.430 2.703 0.786
##
## Cumulative projected inertia (%):
## Ax1 Ax1:2 Ax1:3 Ax1:4 Ax1:5
## 72.43 87.23 95.66 98.37 99.15
##
## (Only 5 dimensions (out of 8) are shown)
##
##
## Eigenvalues decomposition:
## eig covar sdR sdQ corr
## 1 0.25320147 0.5031913 1.102316 1.462761 0.3120711
## 2 0.05174511 0.2274755 1.017318 1.356392 0.1648515
##
## Inertia & coinertia R (Rjuv):
## inertia max ratio
## 1 1.215101 1.427770 0.8510478
## 12 2.250036 2.706504 0.8313439
##
## Inertia & coinertia Q (Qjuv):
## inertia max ratio
## 1 2.139670 3.800487 0.5629991
## 12 3.979469 6.041936 0.6586413
##
## Correlation L (Ljuv):
## corr max ratio
## 1 0.3120711 0.8790003 0.3550296
## 2 0.1648515 0.8158605 0.2020585## RLQ analysis
##
## Class: rlq dudi
## Call: rlq(dudiR = Radu, dudiL = Ladu, dudiQ = Qadu, scannf = FALSE)
##
## Total inertia: 0.2272
##
## Eigenvalues:
## Ax1 Ax2 Ax3 Ax4 Ax5
## 0.112675 0.083210 0.014000 0.008495 0.006291
##
## Projected inertia (%):
## Ax1 Ax2 Ax3 Ax4 Ax5
## 49.583 36.617 6.161 3.738 2.768
##
## Cumulative projected inertia (%):
## Ax1 Ax1:2 Ax1:3 Ax1:4 Ax1:5
## 49.58 86.20 92.36 96.10 98.87
##
## (Only 5 dimensions (out of 8) are shown)
##
##
## Eigenvalues decomposition:
## eig covar sdR sdQ corr
## 1 0.11267484 0.3356707 0.9879998 1.643250 0.2067535
## 2 0.08320955 0.2884607 1.1240015 1.863746 0.1376997
##
## Inertia & coinertia R (Radu):
## inertia max ratio
## 1 0.9761436 1.532974 0.6367647
## 12 2.2395230 2.712636 0.8255891
##
## Inertia & coinertia Q (Qadu):
## inertia max ratio
## 1 2.700272 4.108066 0.6573099
## 12 6.173821 6.921196 0.8920166
##
## Correlation L (Ladu):
## corr max ratio
## 1 0.2067535 0.9773324 0.2115488
## 2 0.1376997 0.9603342 0.1433873Fourth-corner analysis
## [1] "FQ for juveniles"
## [1] "FQ for adults"
With adjusted p-values
## [1] "FQ for Juveniles"## [1] "FQ for Adults"
Combine both approaches
## class: krandtest lightkrandtest
## Monte-Carlo tests
## Call: randtest.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6)
##
## Number of tests: 2
##
## Adjustment method for multiple comparisons: none
## Permutation number: 999
## Test Obs Std.Obs Alter Pvalue
## 1 Model 2 0.3495769 5.294913 greater 0.003
## 2 Model 4 0.3495769 -1.001535 greater 0.841
## class: krandtest lightkrandtest
## Monte-Carlo tests
## Call: randtest.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6)
##
## Number of tests: 2
##
## Adjustment method for multiple comparisons: none
## Permutation number: 999
## Test Obs Std.Obs Alter Pvalue
## 1 Model 2 0.227245 2.1173563 greater 0.032
## 2 Model 4 0.227245 -0.8647113 greater 0.809
The total inertia of RLQ analysis is equal to the SRLQ multivariate statistic defined in Dray and Legendre (2008). This statistic is returned by the fourthcorner2 function:
## Monte-Carlo test
## Call: fourthcorner2(tabR = tempLukeENV, tabL = tempLukeP_juv, tabQ = p_traits3,
## modeltype = 6, nrepet = nrepet, p.adjust.method.G = "fdr")
##
## Observation: 0.3495769
##
## Based on 999 replicates
## Simulated p-value: 0.837
## Alternative hypothesis: greater
##
## Std.Obs Expectation Variance
## -0.9950583 0.5070412 0.0250419## Monte-Carlo test
## Call: fourthcorner2(tabR = tempLukeENV, tabL = tempLukeP_ad, tabQ = subset(p_traits3,
## rownames(p_traits3) != "ATT"), modeltype = 6, nrepet = nrepet,
## p.adjust.method.G = "fdr")
##
## Observation: 0.227245
##
## Based on 999 replicates
## Simulated p-value: 0.782
## Alternative hypothesis: greater
##
## Std.Obs Expectation Variance
## -0.830801471 0.277645441 0.003680229## [1] "juvenile"
## [1] "adult"
“Another approach is provided by the fourthcorner.rlq function and consists in testing directly the links between RLQ axes and traits (typetest=”Q.axes“) or environmental variables (typetest=”R.axes“).”
RLQ axes and traits
## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6, typetest = "Q.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter
## 1 AxcR1 / Climb.0 Homog. 0.9987687707 0.88682739 less
## 2 AxcR2 / Climb.0 Homog. 0.9987476602 0.99016069 less
## 3 AxcR1 / Climb.1 Homog. 0.0008108668 -0.32899201 less
## 4 AxcR2 / Climb.1 Homog. 0.0003319984 -0.98527357 less
## 5 AxcR1 / Erect.0 Homog. 0.0008108668 -0.32899201 less
## 6 AxcR2 / Erect.0 Homog. 0.0003319984 -0.98527357 less
## 7 AxcR1 / Erect.1 Homog. 0.9987687707 0.88682739 less
## 8 AxcR2 / Erect.1 Homog. 0.9987476602 0.99016069 less
## 9 AxcR1 / StemS.0 Homog. 0.0450451117 -0.61118930 less
## 10 AxcR2 / StemS.0 Homog. 0.0476509254 -0.79087050 less
## 11 AxcR1 / StemS.1 Homog. 0.7430481116 2.76091522 less
## 12 AxcR2 / StemS.1 Homog. 0.7086722442 0.69530715 less
## 13 AxcR1 / StemS.2 Homog. 0.1889971996 -0.53878978 less
## 14 AxcR2 / StemS.2 Homog. 0.2372120489 -0.24498835 less
## 15 AxcR1 / StemA.0 Homog. 0.9512348914 2.69794755 less
## 16 AxcR2 / StemA.0 Homog. 0.9558284108 2.64687294 less
## 17 AxcR1 / StemA.1 Homog. 0.0456234804 -1.88476111 less
## 18 AxcR2 / StemA.1 Homog. 0.0427127561 -2.18423441 less
## 19 AxcR1 / Leave.0 Homog. 0.9500246343 2.66787336 less
## 20 AxcR2 / Leave.0 Homog. 0.9545544131 2.61283954 less
## 21 AxcR1 / Leave.1 Homog. 0.0472049444 -2.24577836 less
## 22 AxcR2 / Leave.1 Homog. 0.0436668939 -2.58334353 less
## 23 AxcR1 / MaxStemHeight_m r -0.0056327444 -0.10883613 two-sided
## 24 AxcR2 / MaxStemHeight_m r -0.1036183894 -1.62913691 two-sided
## 25 AxcR1 / MaxStemDia_cm r 0.0585498660 0.43073260 two-sided
## 26 AxcR2 / MaxStemDia_cm r -0.1606342290 -2.95547643 two-sided
## 27 AxcR1 / Under.canopy Homog. 0.8734630866 3.53595591 less
## 28 AxcR2 / Under.canopy Homog. 0.8480620518 0.86129364 less
## 29 AxcR1 / Under.understorey Homog. 0.1260046718 -0.14715570 less
## 30 AxcR2 / Under.understorey Homog. 0.1507807032 -0.08355338 less
## 31 AxcR1 / AverageFruitLength_cm r -0.2271876191 -1.34660127 two-sided
## 32 AxcR2 / AverageFruitLength_cm r -0.0026733621 -0.06479005 two-sided
## 33 AxcR1 / Fruit.large Homog. 0.1822455527 -0.08507815 less
## 34 AxcR2 / Fruit.large Homog. 0.1412713332 -0.71455933 less
## 35 AxcR1 / Fruit.small Homog. 0.7479025293 -0.33449854 less
## 36 AxcR2 / Fruit.small Homog. 0.8584962461 2.26104800 less
## 37 AxcR1 / Consp.conspicuous Homog. 0.3201754800 0.06716201 less
## 38 AxcR2 / Consp.conspicuous Homog. 0.3921603600 2.86361708 less
## 39 AxcR1 / Consp.cryptic Homog. 0.6588325370 1.59024693 less
## 40 AxcR2 / Consp.cryptic Homog. 0.6074045296 1.16697737 less
## 41 AxcR1 / Endem.N Homog. 0.6367268132 -0.85639175 less
## 42 AxcR2 / Endem.N Homog. 0.7368704921 2.45061784 less
## 43 AxcR1 / Endem.Y Homog. 0.3310067021 0.85285614 less
## 44 AxcR2 / Endem.Y Homog. 0.2630461434 0.03652826 less
## Pvalue Pvalue.adj
## 1 0.952 1
## 2 0.884 1
## 3 0.458 0.719714285714286
## 4 0.049 0.308
## 5 0.458 0.719714285714286
## 6 0.049 0.308
## 7 0.952 1
## 8 0.884 1
## 9 0.373 0.863789473684211
## 10 0.298 0.8195
## 11 0.992 1
## 12 0.738 1
## 13 0.325 0.823777777777778
## 14 0.433 0.925692307692308
## 15 0.998 1
## 16 0.996 1
## 17 0.004 0.044 *
## 18 0.005 0.044 *
## 19 0.999 1
## 20 0.996 1
## 21 0.001 0.022 *
## 22 0.002 0.0293333333333333 *
## 23 0.926 1
## 24 0.09 0.44
## 25 0.704 1
## 26 0.007 0.0308 *
## 27 1 1
## 28 0.821 1
## 29 0.508 0.925692307692308
## 30 0.491 0.925692307692308
## 31 0.188 0.636307692307692
## 32 0.945 1
## 33 0.523 0.925692307692308
## 34 0.249 0.7304
## 35 0.337 0.823777777777778
## 36 1 1
## 37 0.552 0.809032258064516
## 38 0.989 1
## 39 0.937 1
## 40 0.878 1
## 41 0.212 0.666285714285714
## 42 0.999 1
## 43 0.814 1
## 44 0.547 0.925692307692308
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6, typetest = "Q.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter
## 1 AxcR1 / Climb.0 Homog. 0.9991347824 0.65487938 less
## 2 AxcR2 / Climb.0 Homog. 0.9986996548 0.61722337 less
## 3 AxcR1 / Climb.1 Homog. 0.0003177235 -0.44855971 less
## 4 AxcR2 / Climb.1 Homog. 0.0005084710 -0.22805059 less
## 5 AxcR1 / Erect.0 Homog. 0.0003177235 -0.44855971 less
## 6 AxcR2 / Erect.0 Homog. 0.0005084710 -0.22805059 less
## 7 AxcR1 / Erect.1 Homog. 0.9991347824 0.65487938 less
## 8 AxcR2 / Erect.1 Homog. 0.9986996548 0.61722337 less
## 9 AxcR1 / StemS.0 Homog. 0.0213369430 -0.71889219 less
## 10 AxcR2 / StemS.0 Homog. 0.0276319001 -0.63837652 less
## 11 AxcR1 / StemS.1 Homog. 0.6665462592 0.33491920 less
## 12 AxcR2 / StemS.1 Homog. 0.6331971702 0.14002055 less
## 13 AxcR1 / StemS.2 Homog. 0.2845234073 0.12382590 less
## 14 AxcR2 / StemS.2 Homog. 0.3202676786 0.32619963 less
## 15 AxcR1 / StemA.0 Homog. 0.9102057866 1.14443704 less
## 16 AxcR2 / StemA.0 Homog. 0.9211187280 1.14962293 less
## 17 AxcR1 / StemA.1 Homog. 0.0611473154 -1.25096409 less
## 18 AxcR2 / StemA.1 Homog. 0.0779316181 0.07817659 less
## 19 AxcR1 / Leave.0 Homog. 0.9094298340 1.41392210 less
## 20 AxcR2 / Leave.0 Homog. 0.9197977076 1.39764104 less
## 21 AxcR1 / Leave.1 Homog. 0.0635809214 -1.04251740 less
## 22 AxcR2 / Leave.1 Homog. 0.0790007011 0.04882859 less
## 23 AxcR1 / MaxStemHeight_m r -0.0624278693 -0.59096454 two-sided
## 24 AxcR2 / MaxStemHeight_m r 0.0884008818 0.93645805 two-sided
## 25 AxcR1 / MaxStemDia_cm r -0.0242877015 -0.15589571 two-sided
## 26 AxcR2 / MaxStemDia_cm r 0.0927305433 1.03739751 two-sided
## 27 AxcR1 / Under.canopy Homog. 0.8111248473 0.96310258 less
## 28 AxcR2 / Under.canopy Homog. 0.7772226093 -0.40410675 less
## 29 AxcR1 / Under.understorey Homog. 0.1868817567 0.24621328 less
## 30 AxcR2 / Under.understorey Homog. 0.2116166257 0.39975532 less
## 31 AxcR1 / AverageFruitLength_cm r -0.0469149117 -0.35465609 two-sided
## 32 AxcR2 / AverageFruitLength_cm r 0.0652052957 0.77729753 two-sided
## 33 AxcR1 / Fruit.large Homog. 0.0914789977 -0.46226195 less
## 34 AxcR2 / Fruit.large Homog. 0.1021589679 -0.36813505 less
## 35 AxcR1 / Fruit.small Homog. 0.8940530723 0.43263672 less
## 36 AxcR2 / Fruit.small Homog. 0.8968200109 0.42873919 less
## 37 AxcR1 / Consp.conspicuous Homog. 0.5144121459 -0.22763547 less
## 38 AxcR2 / Consp.conspicuous Homog. 0.5412733470 -0.08087569 less
## 39 AxcR1 / Consp.cryptic Homog. 0.4832004272 0.27520636 less
## 40 AxcR2 / Consp.cryptic Homog. 0.4511795915 0.09528052 less
## 41 AxcR1 / Endem.N Homog. 0.5800938861 1.29634665 less
## 42 AxcR2 / Endem.N Homog. 0.5403177585 -1.46739872 less
## 43 AxcR1 / Endem.Y Homog. 0.4143389765 1.32691247 less
## 44 AxcR2 / Endem.Y Homog. 0.4568520585 1.52039066 less
## Pvalue Pvalue.adj
## 1 1 1
## 2 1 1
## 3 0.464 0.729142857142857
## 4 0.585 0.745684210526316
## 5 0.464 0.729142857142857
## 6 0.585 0.745684210526316
## 7 1 1
## 8 1 1
## 9 0.234 0.792
## 10 0.295 0.920857142857143
## 11 0.51 0.920857142857143
## 12 0.442 0.920857142857143
## 13 0.666 1
## 14 0.713 1
## 15 0.933 1
## 16 0.942 1
## 17 0.045 0.528
## 18 0.601 0.745684210526316
## 19 0.983 1
## 20 0.985 1
## 21 0.141 0.504307692307692
## 22 0.591 0.745684210526316
## 23 0.586 0.920857142857143
## 24 0.382 0.920857142857143
## 25 0.876 1
## 26 0.331 0.920857142857143
## 27 0.834 0.873714285714286
## 28 0.196 0.792
## 29 0.771 1
## 30 0.798 1
## 31 0.759 1
## 32 0.489 0.920857142857143
## 33 0.442 0.920857142857143
## 34 0.496 0.920857142857143
## 35 0.563 0.920857142857143
## 36 0.552 0.920857142857143
## 37 0.423 0.920857142857143
## 38 0.43 0.920857142857143
## 39 0.584 0.920857142857143
## 40 0.57 0.920857142857143
## 41 0.895 0.895
## 42 0.153 0.748
## 43 0.818 1
## 44 0.858 1
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1RLQ axes and environmental variables
## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6, typetest = "R.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter Pvalue Pvalue.adj
## 1 ELEV / AxcQ1 r 2.754935e-01 1.743928199 two-sided 0.066 0.231
## 2 DIST_TO_EDGE / AxcQ1 r -1.760315e-05 0.007077008 two-sided 0.993 0.993
## 3 CANOPY / AxcQ1 r -9.890480e-02 -1.549484414 two-sided 0.116 0.4212
## 4 TEN / AxcQ1 r -3.881277e-02 -0.655351763 two-sided 0.504 0.756
## 5 FIFTY / AxcQ1 r -3.845224e-02 -0.594885654 two-sided 0.379 0.7218
## 6 CECR / AxcQ1 r 2.706638e-02 0.474041392 two-sided 0.282 0.7218
## 7 UNDER.dense / AxcQ1 Homog. 1.502737e-01 -0.336376590 less 0.59 0.816923076923077
## 8 UNDER.low / AxcQ1 Homog. 2.036597e-01 -0.525871750 less 0.401 0.7218
## 9 UNDER.medium / AxcQ1 Homog. 6.171264e-01 1.702212261 less 0.963 0.974
## 10 ELEV / AxcQ2 r 1.925545e-02 0.133979858 two-sided 0.901 0.974
## 11 DIST_TO_EDGE / AxcQ2 r -1.362020e-01 -2.313959099 two-sided 0.021 0.231
## 12 CANOPY / AxcQ2 r -5.509804e-02 -1.037127674 two-sided 0.325 0.7218
## 13 TEN / AxcQ2 r 1.399334e-02 0.300300278 two-sided 0.742 0.954
## 14 FIFTY / AxcQ2 r 9.046060e-03 0.149636638 two-sided 0.851 0.957375
## 15 CECR / AxcQ2 r 4.142150e-02 0.847226853 two-sided 0.117 0.4212
## 16 UNDER.dense / AxcQ2 Homog. 3.018460e-01 2.340105936 less 0.991 0.993
## 17 UNDER.low / AxcQ2 Homog. 1.929088e-01 -0.974656749 less 0.064 0.384
## 18 UNDER.medium / AxcQ2 Homog. 5.010706e-01 -0.933944686 less 0.298 0.7218
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6, typetest = "R.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter Pvalue Pvalue.adj
## 1 ELEV / AxcQ1 r 0.14022339 1.32154698 two-sided 0.202 0.434
## 2 DIST_TO_EDGE / AxcQ1 r 0.01288337 0.33631748 two-sided 0.779 0.842823529411765
## 3 CANOPY / AxcQ1 r 0.05280187 0.85151475 two-sided 0.434 0.646714285714286
## 4 TEN / AxcQ1 r 0.07951111 1.86534124 two-sided 0.045 0.3744
## 5 FIFTY / AxcQ1 r 0.04350150 1.15331139 two-sided 0.256 0.4608
## 6 CECR / AxcQ1 r -0.04232425 -1.14604755 two-sided 0.249 0.4608
## 7 UNDER.dense / AxcQ1 Homog. 0.17355089 -0.05312864 less 0.489 0.676285714285714
## 8 UNDER.low / AxcQ1 Homog. 0.28645051 1.92488001 less 0.965 0.965
## 9 UNDER.medium / AxcQ1 Homog. 0.53089374 -0.85525175 less 0.2 0.45
## 10 ELEV / AxcQ2 r 0.06836369 0.75587260 two-sided 0.476 0.646714285714286
## 11 DIST_TO_EDGE / AxcQ2 r -0.02305324 -0.64468775 two-sided 0.526 0.676285714285714
## 12 CANOPY / AxcQ2 r -0.08514258 -1.44000659 two-sided 0.168 0.432
## 13 TEN / AxcQ2 r -0.07075257 -1.66212636 two-sided 0.092 0.3744
## 14 FIFTY / AxcQ2 r -0.03532906 -1.01730191 two-sided 0.291 0.523636363636364
## 15 CECR / AxcQ2 r 0.05215427 2.00077290 two-sided 0.03 0.3744
## 16 UNDER.dense / AxcQ2 Homog. 0.18278557 0.22867378 less 0.601 0.68625
## 17 UNDER.low / AxcQ2 Homog. 0.23598540 -0.03940811 less 0.503 0.646714285714286
## 18 UNDER.medium / AxcQ2 Homog. 0.57870228 0.70731698 less 0.796 0.842823529411765
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Results can be represented using a table with colors indicating significance :
## [1] "juveniles"
## [1] "adults"
Significance with axes can also be reported on the factorial map of RLQ analysis. Here, significant associations with the first axis are represented in blue, with the second axis in orange, with both axes in green (variables with no significant association are in black)
## [1] "juveniles"
## [1] "adults"